(CNN) - Pennsylvania Democratic Senate candidate Joe Sestak won an ovation at the weekly Senate Democratic lunch in the Capitol Tuesday, even as questions swirled about his allegation that the White House offered him a job several months ago if he would agree to stay out of a primary battle against incumbent Sen. Arlen Specter.
"I've already answered the questions," Sestak told CNN as he was standing outside the lunch waiting to be introduced. "I have nothing else to say about the matter."
Sestak made similar comments to CNN's John King Monday.
Sestak's refusal to elaborate came as the No. 2 Senate Democrat, close White House ally Dick Durbin of Illinois, called on him to "make it clear what happened."
"Congressman Sestak raised the issue,' Durbin said. "If there's been some confusion, I hope he can make the facts as clear as possible. Then, as far as the administration is concerned, they will react to it."
Sestak did get support from Sen. Bob Menendez, who as head of the Democratic Senatorial Campaign Committee must help Sestak win the general election now that he won last week's primary. Menendez said he doubts anything improper happened if the White House talked to Sestak about a potential job.
"My sense of this is there was probably an inquiry into what kind of public service do you want to perform. What are your interests? And at the end of the day he said I want to be a United States senator from Pennsylvania," Menendez said. "In my mind, that's the beginning of the end of it. I don't' think there is a lot here of great value or really great interest to the people of Pennsylvania."
Asked what Sestak should do to put the issue behind him, Menendez responded, "I think Sestak has to do what he feels is necessary to both clear the air and be able to get forward with the real issues that are important to the people of Pennsylvania."
At a news conference after the lunch, Senate Majority Leader Harry Reid, D-Nevada, said Sestak, a former Navy admiral, gave a "wonderful presentation."
He was introduced by Arlen Specter," said Reid. "There were not questions raised, other than a lot of support."
Should the White House say more about what happened?
"I know nothing about conversations between the Admiral and the White House, if in fact they took place," Reid also said.
Meantime, when Sestak left the lunch, he was followed by a half a dozen reporters who asked several questions about the job offer, but he steadfastly refused to give any additional details.
"Politics is not what I'm interested in," Sestak explained at one point. "I'm interested in one thing, how to change Washington."