He suggested that maybe Obama was the one who should be dumped.
"That's the second-best alternative," he said of replacing Biden. "A better alternative is to make Hillary the [presidential] nominee. As long as we're talking about dumping, let's go to the core problem."
This came amid a nearly hour-long, freewheeling discussion of his views on what he sees as a lack of leadership in Washington, on all sides.
Asked if he was serious that Democrats should dump Obama in favor of the secretary of state, Specter kind of shook his head. "I'm not going to get involved in that selection problem," he said.
Specter said he had no doubt that Obama would - and should - keep Biden. He said the former Delaware senator, a longtime friend, had been "a very effective voice" for the administration.
Still, now that he's out of office, he suggested, he is free to be frank. "I've been on the record a lot," he said. "I'm not running for anything at the moment. Nor do I want anything from anybody."
The White House declined to comment on Specter's remarks, referring the issue to the Obama campaign in Chicago. The campaign said it had no comment.
Specter, with a new book to be released March 27, is making the rounds again after a year of near-public silence.
He has been doing stand-up political comedy - a longtime hobby. (He once compared himself to the borscht belt comic Jackie Mason.)
More significantly, he is launching a public affairs program on Maryland Public Television with $100,000 in sponsorship he raised personally.
He said he hoped that the show - Arlen Specter's The Whole Truth, to be launched Friday - would be picked up nationally by PBS. He chose a Maryland station, he said, to make it easier to lure guests from Washington.
Now 81, the Specter who bantered with the editorial board seemed a bit worn down from the fiery, often testy version who battled Democrat Joe Sestak in the 2010 primary election.