Yeah, more or less. People gripe about it occasionally, especially on the left, but then some shit will go down like Ukraine and suddenly nobody wants to look like an idiot (which will absolutely happen in an American context if you suggest cutting military spending right after Russia invades someone).
It’s not so much public support as the lack of public opposition.
Everyone in “big science” remembers the cautionary tale of the Superconducting Super Collider, which was cancelled mid-project when it became politically viable to oppose it as a waste of money. The circular tunnel is still sitting dusty and abandoned down in Texas while CERN runs another round on the LHC.
Big results that gather public praise go a long way toward making sure the next big science project will at least be seriously considered.
Global force projection at the benefit for all Western economies is very expensive. This money is required to even allow the form of economy "the West" is running.
How else were you going to keep up the Pax Americana that enables globalization by making significant global trade networks even possible in the first place? Who's gonna insure your freighter if international waters aren't protected by Western navies? Pirates, rogue states closing important channels, at will seizures for no reason... the list is long.
As the Pax Americana will likely soon fade through growing influence of the BRICS nations and "America First"-style ideologies, the 700B will probably wither away quite fast in the next decades - along with all the benefits we enjoyed since WW2.
Just one illustration. How man South American or African nations support the sanctions against Russia? How many Asian nations that are not Japan?
Public support for NASA drives the members of Congress to allocate funds for its work. So, NASA spends a whole lot of effort showing the public how cool its work is. That, and it divides its facilities and subcontractors across the various states to ensure that every member of congress has constituents who benefit from its payroll.
> is there public support for the >$700B a year spent on the military?
Of course. It's tempting to think we're in this new lovey-dovey age of an improved/superior humanity, but the reality is man's baser instincts are kept in check by BFGs and MAD.
> stunning images was enough to get the public to support a $10B project.
I don't believe public support is relevant; is there public support for the >$700B a year spent on the military?