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And Judson Phillips, leader of Tea Party Nation, questioned Mr. Rove’s own political skill at picking electoral winners, saying that donors to American Crossroads would have been better off investing with Bernie Madoff, the man behind the largest Ponzi scheme in history.

“I think Karl Rove should take a long overdue retirement back to his home in Texas, where he should not be seen or heard from again,” Mr. Phillips said.

Amy Kremer, Tea Party Express chairwoman, said Mr. Rove’s effort threatens to “water down the brand” because he is willing to support “RINOs” (“Republican In Name Only”) as long as it edges the party closer to a majority.

Mrs. Kremer said she would rather have had Christine O’Donnell stick to her principles and lose her 2010 Senate race in Delaware to Democrat Christopher A. Coons than to have had Rep. Mike Castle, a moderate, win it.

“He is willing to sacrifice principle for power, and we are not going to sacrifice on that,” Mrs. Kremer said. “There are Republicans that are just as responsible as Democrats are for this out-of-control spending, and we need people who are willing to rein it in.”

But Fred V. Malek, a former assistant to Presidents Richard Nixon and George H.W. Bush, defended Mr. Rove’s latest political venture as a way to maintain the GOP’s viability as a national party.

“If you are going to have a majority, you are going to have to have some pragmatism and realize there are states where a moderate candidate is the only candidate that can win and that candidate is going to be a hell of a lot more conservative than the Democrat that is going to be elected,” Mr. Malek said. “I go back to what Ronald Reagan said. I don’t expect people to agree with me 100 percent of the time, 75 percent is just fine. I would much rather have senators or congressmen that are labeled as moderate Republicans than have a Democrat who agrees with me 10 percent of the time.”

H.W. Brands, a history professor at the University of Texas, said the current fight reminds him of the battle between the Barry Goldwater and Nelson Rockefeller wings of the party in the 1960s, which “was wasn’t resolved until Reagan came along.”

“The takeaway from that for this fight is that the quarrel doesn’t really end, but can be papered over by a charismatic candidate,” Mr. Brands wrote in an email. “If the Rs had nominated a more appealing candidate last summer they would have won in November and wouldn’t be having this fight. Winning cures lots of ills — at least temporarily. But the purist-pragmatist dispute is always with us. It’s the essence of politics.”