The administration is taking it seriously, but so far has had trouble getting the funds for it as well as fully convincing the Pentagon that a 6th force, separate from the Air Force, is really needed.

The motivating enemy is apparently...

In 2007, China blew up a dead weather satellite with a missile, creating a massive debris cloud in orbit, which Pence called "a highly provocative demonstration of China's growing capability to militarize space".

As for the infighting and funding...

But the monumental task of standing up a new military department, which would require approval by a Congress that shelved the idea last year, may require significant new spending and a reorganization of the largest bureaucracy in the world.

And the idea has already run into fierce opposition inside and outside the Pentagon, particularly from the Air Force, which could lose some of its responsibilities.

Defense Secretary Jim Mattis last year said he opposed a new department of the military "at a time when we are focused on reducing overhead and integrating joint warfighting functions."

This week [of Aug 10], Mattis said the Pentagon and the White House "are in complete alignment" on the need to view space as a warfighting domain. But he stopped short of endorsing a full-fledged Space Force. [...]

The White House intends to work with lawmakers to introduce legislation by early next year, a senior administration official said, with the hope of standing up the first new military department since the Air Force was formed in 1947. [...]

Some members of Congress advocated last year for creating a Space Corps in the Air Force Department, similar to how the Marine Corps is part of the Navy Department. Elevating the proposal to create a new department will mean additional Pentagon bureaucracy, critics say. [...]

Before Trump's announcement in June that he wanted a Space Force, Mattis and Air Force Secretary Heather Wilson had cautioned against creating new Pentagon bureaucracy to address space issues. James said she thinks they're now "stuck because the president announced this by surprise."

Gen. David L. Goldfein, the Air Force's top officer, and Gen. Stephen Wilson, the vice chief, sat quietly in the Pentagon auditorium as Pence spoke.

Air Force Gen. Paul Selva, the Pentagon's vice chairman of the Joint Chiefs of Staff, said in a briefing with reporters that the Pentagon is very much in favor of establishing a Space Command as a way to speed up efforts in space.

But when it comes to establishing a new branch of the military, Selva said, "there's an obligation" to present a set of options that can be presented to Congress.

A list of people who are likely to take this idea seriously:

• A subset of Pentagon brass that will see it as opportunity for better advancement, empire-building (in a bureaucratic sense), and influence. Anytime something like this exists, there are bosses who run the show. People want to be those bosses.




• A subset of aerospace and other contractors who are either already defense related vendors, or hope to be under the new initiative.



• 
  

  People (either military, or lay people, or politicians) who legitimately worry about China's - and secondarily other potential adversaries' - space and especially anti-space capabilities.

  
  
  

  Fizz's answer covered that, but as an interesting summary source, a recent StratFor podcast on history of war in 20th century had a tail end discussing this specific topic at a very high level.

  
  
  

  To summarize,

  
  
  

  • Virtually our entire military edge at the moment (from direct combat technology, to command and control, to logistics) heavily depends on satellite constellations.

  
  

  • For that matter, our civilian economy - which drives US military power (as has been proven ever since the Hundred Years' War and re-proven in WWI and WWII) depends on them too.

  
  

  • China and some others like Russia exhibited both desire and meaningful progress in ASAT capabilities that can easily render these edges null and void.

  
  

To bring this more on topic with Politics.SE and not Space.SE, a couple more political points:

• I have also heard multiple assertions (don't recall the source but I'm itching to say 538 podcast? Or Arms Control Wonk or The Diplomat?) that this is a political maneuver by Trump administration, to grab attention onto a new topic. Regardless of whether that accusation is true or not, it is being taken seriously by those making it.




• I have also heard ideas that this is potentially somewhat of an imprecise equivalent of Moon Race. Just as the moon race did, it could offer both a way to inject money into US economy; and produce sustainable long term gains via R&D; and offer domestic political lift ("because Bruce Willis and Ben Affleck", if no other angle).

To rebut some points that make this question somewhat biased:

• 
  

  
  

  Space travel isn't cheap

  
  

  
  
  

  First, the curve is sharply sloping down. Between microsats, and new space technologies being developed as part of private space "mini race" by people like Rutan, the costs are coming down drastically. That doesn't even go into Elon Musk level of futuristic tech-fi plans.

  
  
  

  Second, when the downside of not doing this is literally every single civilian and military advantage US has being easily destroyed, with very real probability of major disruptions to civilian economy and life because of supply chain issues, the costs suddenly become more worth contemplating.

  
  


• 
  

  
  

  There aren't "enemies" in space.

  
  

  
  
  

  Other answers covered it in details. But someone forgot to tell that to Russia, China, and - once they have enough tech to achieve this - even Iran/DPRK/etc... Obviously, China thinks your assertion is wrong on many levels.

  
  


• 
  

  
  

  The potential dangers that could come from space, asteroids or solar failure or, more realistically, solar flares aren't issues specific to a nation

  
  

  
  
  

  And yet, other nations don't seem to be interested in allocating resources to pay for such threat reduction to the best of my knowledge. I'm tempted to quote from Tusk's anti-Trump speech, about "sometimes the only helping hand you find is at the end of your own arm."

  
  

This is not from me but from someone purportedly in the Air Force familiar with space related affairs:

I'm in the part of the Air Force that will become the Space Force. [...] The rationale behind the Space Force/Corps is that the Air Force is mismanaging it in favor of air things. All the generals and upper leadership of the Air Force come from an air background. They routinely pilfer our space coffers to pay for more F-35esque boondoggles while they let Russia and China edge ever closer to space parity with us. They’ve repeatedly implemented “measures” meant to console people upset by this but nothing changes. Everyone has a story about some general asking you to do something physically impossible with space infrastructure because they fundamentally do not understand it. The idea is (and it was around a long time before trump) that an independent or semi-independent branch would be more efficient and cheaper doing the same things because all the people in it would be raised with a space background rather than an air one. The generals down to the janitors would be space professionals with an understanding of global satcom, pnt, spacelift, and orbital mechanics. Nobody would be able to basically rob us and make us use literal 40 year old computers. It’s literally an organizational restructuring, a bunch of guys from the Air Force/Army/Navy will just swap their nametapes to read Space Force and nothing else will change.[...].

• Space travel isn't cheap, but the costs are coming down. Basic access to space costs in the thousands, not millions of dollars. Many nations have the ability to place significant payloads in orbit.




• There are enemies in space. Many nations are investigating anti-satellite technology (based on EMP). China and Russia and the USA are all developing weapons that can be delivered from space or can be used to target satellites.




• There are resources in space that could be worth fighting over. Asteroid mining is seriously considered. When trillions of dollars of raw materials are available, we may expect the possibility of conflict.

Relevant sources: CNN The race to militarize space, Wikipedia Space Warfare

A Rasmussen telephone survey reveals that 33% of Americans support Space Force, 40% oppose, and 27% are not sure.
http://www.rasmussenreports.com/public_content/politics/general_politics/june_2018/33_support_creating_a_national_space_force

Support for Space Force is lower than Donald Trump's general approval rating, which tends to be around 41%. This is a bad sign, since most of his followers support all of his policies.
https://news.gallup.com/poll/203207/trump-job-approval-weekly.aspx?g_source=link_newsv9&g_campaign=item_201617&g_medium=copy

America has something called Air Force Space Command, which likely renders an entirely new Space Force military branch superfluous. The wikipedia page for AFSPC states "[AFSPC] is the primary space force for the U.S. Armed Forces." It turns out that if a Space Force were to be authorized by congress, it would not accomplish any missions that are not already underway. It would simply reorganize the Pentagon by splitting the Air Force into two separate branches. While the second link that follows will reinforce these points, it also points that voting on Space Force logos is currently being used by Trump to solicit donations for his 2020 campaign, which could be considered an unethical use of the office.
https://en.wikipedia.org/wiki/Air_Force_Space_Command
https://www.theatlantic.com/politics/archive/2018/08/the-space-force-branding-trump-logos/567173/

Subjectively, I would say that Space Force has attracted a lot of satire and ridicule relative to most other presidential positions. Michael Kosta, Trevor Noah, Stephen Colbert, Seth Myers, Jimmy Kimmel, Stephen King, Jim Carrey, and others have joined in on the ridicule. Of all Trump branding, this brand seems one of the most open for satire; particularly because the branding focuses on space (an unlikely near-term battleground) rather than satellite and missile defense. So the branding seems to miss the mark, and the name suggests an enterprise that most Americans would doubt we need in the short-term (combat in the actual vacuum of space beyond Earth's orbit). So my subjective read on American sentiment is that somewhat more than a majority of the country does not take Space Force seriously.
https://www.youtube.com/watch?v=LYQX-BPUqN4

If our aim is to prepare for war, then we need to focus more on space warfare than we currently are. Whether or not we ultimately need a "Space Force," or whether we simply need to ensure that our Air Force is focused enough on space, is up for debate. But the idea is taken somewhat seriously, yes.

Why Would We Need a U.S. Space Force, Anyway?

We currently have a wide variety of space-related military efforts, but they are spread out over a multitude of different departments of the military, making them less efficient and focused:

Disparate space-related efforts are scattered across the Army, Air
Force, and Navy, not to mention intelligence officers, National
Reconnaissance Office and Space and Missile Systems Center. Doug Loverro, a former DoD Deputy Assistant Secretary of Defense for Space Policy, noted that fighting in space is different than fighting anywhere else, in the same way that the Navy prepares for unique combat at sea. “We lack that focus for space, one of our five main warfighting domains,” he said.

If war were to break out, we would have a significant problem communicating with our troops:

These threats, Loverro said, are already here. If a war broke out in the Pacific, commanders would have a hard time communicating with troops. “We have a SATCOM jamming threat today,” Loverro told Congress. “We have nothing on books until 2027 to solve that problem.”

Other countries are prepared to attack our satellite infrastructure if it comes to war:

Gen.Kehler said the stakes are high because the loss of critical assets in space could prove decisive in a future battle. Potential enemies know this and have been investing in weapons on the ground or in space to take out or jam satellites. “Time is not on our side,” he said.

There is some disagreement as to whether we actually NEED a space force, rather than a new focus, new ways of thinking, and better organization:

Loverro ... concedes a new service may not be needed. “We don’t need to move it from the USAF to create the space smart-force we need,” he said.

I can say that there are many Americans who are of the opinion that asking a current branch of the U.S. military to promote "new focus, new ways of thinking, and better organization" would be a lot to ask of such a large, entrenched bureaucracy.

tl;dr: From the correct perspective, this is nothing but positive all around.

As is well-established, US policy correlates more with the interests of small elites and special interest groups than with the public's preferences. With this perspective in mind, and considering the influence of the military-industrial and intelligence-industrial complexes, a Space Force is a swell idea - as I will elaborate in a tongue-in-cheek, but still basically serious, manner:

Space travel isn't cheap.

Great! more contracts for aerospace and defense contractors.

There aren't "enemies" in space.

Great! This means the funding won't depend on the US being in war with anybody, so there will be less pressure to reduce it if the US "wins" or "loses".

The vagueness of what constitutes conflict or enmity in space, and the lack of territorial demarcations, also makes it easier to portrary the actions of other world states as belligerent or hostile: "The Russians may try to hack our election systems... from SPACE"; "The Iranians are trying to blind our satellites" (this may have actually happened once); "The Europeans are trying to monopolize space"; "The Chinese space program is a fundamental threat to our national security".

The potential dangers that could come from space, asteroids or solar failure or, more realistically, solar flares aren't issues specific to a nation.

Great! That means that the US Space Force can ignore the actual dangers in space and won't actually need to do anything. And this, in turn, means it will be almost impossible for it to fail.

Also the United States is a formal signatory of the Outer Space Treaty, which prohibits many conventional and unconventional military activities. (Thanks, TylerH)

Now, this is slightly tricky. The US can go in one of several routes here:

• It can just waste the budget on things that comply with the treaty, and not actually bring up any combat-capable spaceships or battle space-stations. In the extreme version of this approach, it doesn't actually have to do anything other than put its stickers on some NASA rockets and vehicles and not actually launch anything into space.


• It can ignore the treaty, like it ignores the UN charter, the sovereignty of various states, the rulings of the International Court of Justice (which found it to have unlawfully intervened in Nicaragua's internal affairs; Nicaragua's awarded reparations from the US were never paid), etc. There will be complaints from China, Russia, Iran, and probably even European states, but, if they can stomach US military intervention at a whim almost anywhere, they'll probably live with this too.


• It can withdraw from the treaty. Trump has done so with the JCPOA (the multi-partite Iran "nuclear deal"), without providing any valid cause to my knowledge, so why not this treaty as well?