The answer depends on some missing facts. The first is, who do you get the footage from. For the sake of discussion, I will assume this is from C-Span. This matters because under US copyright law, works of the US government are not protected by copyright, but that does not mean that works about the US government are unprotected. C-Span is not a government employee, therefore C-Span is entitled to copyright protection. The C-span FAQ suggests a complex of considerations related to the need for a license.
The House of Representatives can establish its own rules which could prohibit making a recording of sessions with the intent to make political comments on the content, but those rules can only pertain to conduct in the House chambers. The house cannot unilaterally pass a law, that requires cooperation of the Senate and the president, or massive cooperation of the two houses, and such a law that prohibits political commentary on House conduct would not long survive judicial review. The C-span FAQoid does not suggest that there is any restriction on political usage of their footage, so perhaps the footage comes from somewhere else.
The main point is that you would have to dig deep to see who is distributing the footage, and under what authority they impose restrictions on redistribution. Ordinary copyright could be the source, though it is also an open question whether automatically recorded video has the scintilla of creativity required to make a work protectable.
Another possible source is the Library of Congress, which unlike C-Span is full of government employees creating government works (which are unprotected). They do say that there is a form that has to be signed avowing that you will not use the work for political or commercial purposes. In order to find out what their requirements are, you have to call or mail an exact order, which will be forwarded to another office, and you will get the required form. Again, though, it is an open legal question whether a branch of the US government can prohibit making political comments about congressional sessions. It is a little less controversial that Congress can regulate interstate commerce.
If a person actually holds copyright in a work, the question of commercial / non-commercial and fair use does not come down to a simple commercial / non-commercial dichotomy. Furthermore, "non-commercial" is not the same as "free". Two opposites on the "nature of the work" continuum are "educational" vs. "commercial", but vast numbers of educational works cost money. If you were to freely distribute the entirety of a recent commercial movie, that would be a "non-commercial" use, but also highly infringing. If you extract 2 seconds from said film, that might be fair use. If you sell copies of that extract, that works against a fair use analysis.
