Can Congress force television cameras on the Supreme Court?

The L.A. Times reports on a bill that would impose television cameras on the Supreme Court:

Under [Sen. Arlen Specter's] proposal, which he introduced last month, cameras would be removed only if a majority of the justices determined that their presence would undermine the due process of a litigant in a specific case....

The public affairs network C-SPAN broadcasts gavel-to-gavel coverage of House and Senate floor sessions, and the network's Chairman and Chief Executive Brian P. Lamb told the Judiciary Committee that he had written to Chief Justice John G. Roberts Jr. offering similar coverage of the high court.

"The judiciary has become the invisible branch of our national government as far as television news coverage is concerned — and, increasingly, as far as the public is concerned," Lamb said.

I would very much like to see the oral arguments on television, but I don't think Congress ought to be imposing it on the Court. At least two of the justices -- Scalia and Souter -- have strongly opposed cameras in the Supreme Court. I should think there is a decent argument that this would be unconstitutional, violating separation of powers.