This isn't at all my area, so what follows is just amateurish speculation. But off the top of my head I would think the answer is clearly "yes." Congress has a great deal of control over how the Court operates. For example, Congress determines the number of Justices, see 28 U.S.C. § 1, when the Term opens, 28 U.S.C. § 2, and allowances for law clerks, 28 U.S.C. § 675. Congress also requires that the Court's opinions must be bound togther and published as volumes of the United States Reports "as soon as practicable after rendition." 28 U.S.C.A. § 411. As far as I know, none of these sorts of regulations have ever been suggested to violate the Constitution.
The only counterargument I can think of is that perhaps control over broadcasting proceedings is somehow part of "the judicial power." The Constitution explicitly states that "the Judicial Power of the United States, shall be vested in one supreme Court," Article III, Section 1, and if the Constitution vests the judicial power in the Court then Congress cannot take it away. But I have always understood the notion of "judicial power" to mean the power to decide cases and controversies, Cf. Murray' Lessee v. Hoboken Land & Improvement Co., 18 How. 272 (1856), not the power to hear oral arguments in a setting that is more or less public.
As I said, though, this isn't my area; I hope those who work in this area can chime in.
UPDATE: Marty Lederman weighs in here.
Related Posts (on one page):
- Justice Kennedy Argues for a Judicial Pay Increase and Against Allowing TV Cameras in the Supreme Court:
- Can Congress Force the Supreme Court to Televise its Oral Arguments?
- Can Congress Force the Supreme Court to Televise Proceedings?: