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“I don’t think the burden should be on me,” he said in a telephone call with Nevada reporters last week. “The burden should be on him. He’s the one I’ve alleged has not paid any taxes. Why didn’t he release his tax returns?”

Reid spokesman Adam Jentleson, in email Sunday regarding the attacks on Mr. Reid, said the unnamed source is “extremely credible” and accused Republicans of trying to “cover up for Mitt Romney’s stonewalling.”

“This issue is not going away until Romney decides to be straight with the American people and release his tax returns,” Mr. Jentleson said.

But late last week, Mr. Romney himself emphatically said he would not release the returns and dared Mr. Reid “to put up or shut up.”

Harry’s going to have to describe who it is he spoke with, because of course that’s totally and completely wrong. It’s untrue, dishonest, and inaccurate. It’s wrong,” he told Fox News’ Sean Hannity on his radio show. “So I’m looking forward to have Harry reveal his sources and we’ll probably find out it’s the White House.”

No Democrat appearing on Sunday’s news talk shows disavowed Mr. Reid’s comments, which Republicans said last week smacked of McCarthyism in their use of anonymous sources to make insinuations that the accused must then disprove.

Rather than disavowing Mr. Reid’s claims, most Democrats instead tried to turn the conversation away from him and instead on Mr. Romney.

David Axelrod, Mr. Obama’s senior campaign adviser, told “Fox News Sunday” that he didn’t know the identity of Mr. Reid’s source but that “Gov. Romney can resolve this in 10 seconds. They can release the tax returns.”

Robert Gibbs, an adviser to Mr. Obama and his former press secretary, was asked on CNN’s “State of the Union” whether Mr. Reid should tamp down his accusations against Mr. Romney. “I don’t think anybody controls Harry Reid,” was his reply.

When pressed again by show moderator Candy Crowley whether Mr. Reid should drop the issue, Mr. Gibbs said instead that “Harry Reid isn’t the one who’s made this debate. Mitt Romney has brought this to the fore.”