Republicans on Sunday escalated their attacks on Senate Majority Leader Harry M. Reid (D) over his claim that presumptive GOP presidential nominee Mitt Romney did not pay taxes for years, with the Republican party head calling Reid a “dirty liar.’’

Republican National Committee chair Reince Priebus, speaking on ABC’s “This Week,’’ contrasted Reid’s allegations relating to Romney’s wealth with Reid’s own lifestyle as a resident of the Ritz-Carlton hotel in Washington, where he lives.

“As far as Harry Reid is concerned, listen. . . . I’m not going to respond to a dirty liar who hasn’t filed a single page of tax returns himself. Complains about people with money but lives in the Ritz-Carlton here down the street,” Priebus said. “. . . This is just a made-up issue. And the fact that we’re going to spend any time talking about it is ridiculous.”

Reid created a political dustup last week by suggesting that Romney is withholding his tax returns because he didn’t pay taxes over a 10-year stretch, part of Democratic efforts to focus on Romney’s wealth and pressure him to release more than two years of returns. Romney forcefully rejected the allegations on Friday, saying he paid “a lot of taxes” every year and that Reid should “put up or shut up.’’

Reid spokesman Adam Jentleson struck back at Priebus on Sunday, calling Romney “the most secretive candidate since Richard Nixon.”

“Republicans can try to cover up for Mitt Romney’s stonewalling all they want, but this issue is not going away until Romney decides to be straight with the American people and release his tax returns,’’ Jentleson said.

Jentleson also doubled down on Reid’s original allegation, in which the senator told the Huffington Post that he had learned of Romney’s tax history from “a person who had invested with Bain Capital,” Romney’s former firm. Reid, who has a history of making incendiary statements about Republicans, declined to identify the investor or cite proof for his allegation.

In his statement Sunday, Jentleson reiterated: “As Sen. Reid has said, an extremely credible source informed him that Mitt Romney did not pay taxes for 10 years. . . . It’s clear Mitt Romney is hiding something.’’

Democratic National Committee chair Rep. Debbie Wasserman Schultz (Fla.), also appearing on “This Week,” echoed that theme Sunday, declining to criticize Reid and saying that Romney is at fault for the confusion over his wealth.

“I do know that Mitt Romney could clear this up in 10 seconds by releasing the 23 years of tax returns that he gave to John McCain when he was being vetted for vice president,” Wasserman Schultz said. “Or even 12 years of tax returns that his own father said were what was appropriate.’’

On “Fox News Sunday,’’ U.S. Senate candidate Ted Cruz (R-Texas) said his big primary victory last week over a better-known establishment candidate reflected “a tidal wave that’s sweeping the whole country, which is that voters are tired of career politicians in both parties.’’

Cruz, who won with strong support from the tea party movement, predicted that Romney — who has periodic trouble winning over conservatives — will gain overwhelming support in the November election from tea party and other conservative activists. “I have spoken to literally thousands and thousands of tea party activists,’’ Cruz said. “I have yet to meet a single tea party leader that is not going to vote for Mitt Romney and work for him because our country is in crisis. And we’ve got to stop this Obama agenda if we’re going to preserve opportunity for our kids and grandkids.’’