Senators are renewing calls to televise Supreme Court proceedings. Their theory is that the Supreme Court requires the scrutiny of daytime TV in order to do a good job. Also, as the Justices are making more frequent appearances on TV (such as the Breyer-Scalia debate of a few months ago), they should just have TVs in the courtroom anyway. The Court currently releases same-day audiotapes and transcripts of its proceedings, and every filed piece of paper in the Court is available to the public.
Article I limits the powers of Congress. Nowhere in it does Congress have the power to regulate the Supreme Court or its internal functions; it may only give advice and consent to the appointment of Justices. The justices have lifetime appointments for good behaviour, salary protection (including against inflation) and are generally allowed very little oversight by the other branches. Article III allows Congress to ordain and establish inferiour courts. The Framers had the wisdom to vest power in three separate branches of government. Even the Madisonians, who believed the judiciary to be the weakest branch of government as it lacks both a purse and a sword, did not desire this micromanagement by Congress.
Ultimately, any Constitutional challenge to this provision will be decided by the Supreme Court, rendering it effectually their decision anyway (albeit one without the presumption of validity that the Court should have over its own daily operations). As such, it is short-sighted of Mr. Specter to attempt to force this issue via passage of a law instead of a friendly discussion over at One First Street. If he does not receive an audience there, perhaps it is because the internal functioning of another branch of government is not quite his business anyway.