The issue of facilitating the public's ability to see and hear what happens inside the Supreme Court has percolated for a number of years.
Advocates say that televising oral arguments would be consistent with the (generally) open nature of the American judiciary, while opponents (not least among them, several current Justices who adamantly oppose cameras) argue that they would demean and possibily delegitimize the process.
Certainly the trend is toward increased access for the public: voice-recordings of an increasing number of oral arguments are now made available, with the Justices' tones and sentence structure analyzed everywhere from NPR to Fox News. It will be interesting to see how long the Court will be able to buck the societal trend of everything -- and everyone -- being on television.
Here's a portion of Specter's argument:
"I believe Congress has the authority, should it choose to do so, to direct the Supreme Court to permit its proceedings to be televised ... The Supreme Court, in a series of cases, has said the public has a right to know what is going on inside the courtroom ... well, in an electronic era, where the public gets so much of its information via television or via radio, there ought to be that access."