Can Congress force the Supreme Court to permit television cameras during open sessions?

Tony Mauro has an interview with Senator Specter discussing this topic:

The Senate Judiciary Committee in April approved two Specter-sponsored bills on cameras in the high court. One, S. 446, would require the Court to allow cameras, while the other, S. Res. 339, would merely urge the Court to do so. At the time, Specter indicated he would press for the resolution first as a more modest approach that would win passage more easily.

The precatory resolution, S. Res. 339, seems cool enough. It is merely advisory (like the Sentencing Guidelines!) But what about the mandatory bill? Here is the text of the mandatory bill, S. 446:

‘The Supreme Court shall permit television coverage of all open sessions of the Court unless the Court decides, by a vote of the majority of justices, that allowing such coverage in a particular case would constitute a violation of the due process rights of 1 or more of the parties before the Court.’.

That is quite a tough standard–the coverage would have to “constitute a violation of the due process rights” of a party? I can’t imagine that being satisfied too often.

I previously queried whether Congress could force the Court to open the Supreme Court doors.

I can’t imagine the Court would have the chutzpah to tell the Congress “Cameras? We don’t need no stinking cameras.” But, from a purely hypothetical separation of powers perspective, what could the Congress do if the Court tells them to buzz off. Sue them? Ha! Deny funding? Probably. Would this fall under the Congress’s power to make rule pertaining to the Court? Not sure.