Rep. Joe Sestak, the brand-new Democratic nominee for the U.S. Senate from Pennsylvania, and White House press secretary Robert Gibbs each dodged questions Sunday about Sestak's claim that the Obama administration offered him a job last summer if he would skip a primary challenge to Sen. Arlen Specter.

The issue, with implications of potential illegality by the White House, has rekindled in the five days since Sestak defeated Specter, who fled the Republican Party to seek a sixth term. GOP leaders are pressing Sestak and the administration to provide details of discussions.

During an appearance on NBC's Meet the Press, Sestak confirmed he was offered a job. But he would not answer host David Gregory's follow-up questions. "Anything that goes beyond that is for others to talk about," Sestak said.

On CBS's Face the Nation, Sestak said that providing details "just gets into politics, and actually that is what I think is failing Washington, D.C."

Gibbs, bombarded with questions about the allegation at Wednesday's press briefing, acknowledged that there were talks with Sestak about his challenge to Specter but told host Bob Schieffer on Sunday that they were kosher.

"Lawyers in the White House and others have looked into the conversations that were had with Congressman Sestak - and nothing inappropriate happened," Gibbs said. "I'm not going to get further into what the conversations were."

After beating Specter 54 percent to 46 percent Tuesday, Sestak faces Republican Senate nominee Pat Toomey in the fall general election.

Sestak, a retired Navy admiral who is in his second term in the House, appeared on the two political talk shows as analysts grappled with primary electorates in Pennsylvania and Kentucky that gave the boot to a Democratic incumbent (Specter) and the GOP establishment choice (Trey Grayson, who lost to Rand Paul).

Because the White House backed Specter, who had provided the crucial vote for President Obama's $787 billion economic stimulus, Sestak was cast as the outsider. Under questioning from Gregory on Meet the Press, however, he had difficulty naming any policy disagreements with the administration.

Sestak voted for bailouts of the financial industry, the stimulus, the health-care overhaul, and a bill designed to cap carbon emissions to battle climate change - all Obama priorities.

"Oh, I honestly think that this president has done great, good things, but I don't think we've gone far enough in terms of helping small business," Sestak said.

Toomey's campaign seized on the interview to argue that Sestak is a loyal Obama Democrat and thus out of step with the public in a state where about half of voters disapprove of the job the president is doing, according to the most recent independent polls.

"It is clear that Joe Sestak is not an independent voice for Pennsylvania, but an echo," said Nachama Soloveichik, communications director for Toomey. Sestak has voted 100 percent of the time this year with House Speaker Nancy Pelosi (D., Calif.), she said.

There was no secret that the Obama administration and Democratic leaders in Pennsylvania wanted to avoid a divisive primary fight and rally around Specter. But Sestak refused to stand down, and then caused a stir in February when he told veteran TV journalist Larry Kane that he had been offered a significant federal job to forgo a challenge. Kane asked whether the post was Navy secretary, and Sestak declined to comment.

He has stayed mum since on the details of the job claim, and the White House, when it would address the subject at all, has said nothing inappropriate happened.

Rep. Darrell Issa of California, the top Republican on the House government-oversight committee, has demanded information from the administration on conversations with Sestak, and he has called for an independent counsel to investigate the matter. He has been rebuffed on both counts.

Last week, Issa said he was considering filing a formal ethics complaint against Sestak on grounds that he has withheld knowledge of a potential crime.

"President Obama faces a critical choice - either he can live up to his rhetoric of transparency and accountability and disclose who in his White House tried to manipulate an election by bribing a U.S. congressman, or he can allow his administration to stonewall and relinquish the mantle of change," Issa said Sunday in a statement.

Even Democratic National Chairman Tim Kaine, appearing on Fox News Sunday, seemed to suggest that the White House should be more forthcoming.

"Look, if the question gets asked, it's something they should deal with," Kaine said. But when he was asked later, on ABC's This Week, whether the White House had an obligation to provide details, Kaine said: "I don't know that they do."

Contact staff writer Thomas Fitzgerald at 215-854-2718 or tfitzgerald@phillynews.com.