Still, he has clearly been staggered this week by an advertisement released by Mr. Sestak showing former President George W. Bush praising Mr. Specter as a “firm ally.” That is precisely the kind of advertisement Democrats are planning to use against Republicans this fall. Democrats and some of Mr. Specter’s supporters said the advertisement, which also shows the senator appearing alongside Sarah Palin and a clip of Mr. Specter arching an eyebrow as he declared, “My change in party will enable me to be re-elected,” was crystallizing concerns about him among both Democratic partisans and voters weary with Washington. “It’s been a rugged time, candidly,” Mr. Specter said.

The most likely Republican candidate, Pat Toomey, a former member of Congress and former head of the Club for Growth, a conservative organization, helped drive Mr. Specter from the Republican Party. But some of Mr. Specter’s supporters say that Mr. Specter would be a much stronger candidate than Mr. Sestak, a retired Navy admiral, against Mr. Toomey in the fall.

“I am firmly of the belief that Arlen Specter is head and shoulders above anyone else in his ability to lead us to victory this November,” T. J. Rooney, the head of the Pennsylvania Democratic Party, said Tuesday. “Arlen Specter knows how to beat Toomey: he has done it before.”

Mr. Rooney pointed to Mr. Sestak’s unconventional campaign manner — “He doesn’t have a campaign manager!” he said — and said that Mr. Specter is a tougher campaigner who could appeal to independent voters and moderate Republicans, who he said would be lost to Mr. Toomey if Mr. Sestak won.

Mr. Rooney also suggested that Mr. Sestak would be hurt in a general election campaign by an issue raised in advertising and on the campaign trail by Mr. Specter: the circumstances of Mr. Sestak’s retirement from the Navy.

A report at the time said Mr. Sestak had created “a poor command climate.” Mr. Sestak said he was simply carrying out a tough assignment, assessing the Navy’s fleet to recommend cutbacks, and he has refused Mr. Specter’s demands that he release his records.