Let me anticipate two questions.
C-Span is not a government entity, but a not-for-profit consortium backed by the cable industry, and, all other things being equal, can own and assert copyright.
Second, a congressperson showing a bit of C-Span footage of a congressional hearing on the congressperson’s website, would seem to be fair use.
OK, C-Span asked Speaker Pelosi to remove a clip of its coverage of a House committee hearing on global warming from her blog. This apparently after Republicans accused Pelosi of violating C-Span copyright.

Now C-Span has changed its policy to allow the Speaker of House to show footage of congressional hearings on her website.
Schoolhouse Rock materials available here.