C-SPAN allows teachers at accredited institutions to record and use any program as long as it is for in-class educational use and not redistribution or political purposes.
Video coverage of floor proceedings in the House and Senate are in the public domain; no permission is needed. Hearings may or may not be, then the permission above would apply.
Some other cable networks offer some form of permission. It's always best to check the network's web site for the information about use, or ask for specific permission.