Rep. Peter King, R-N.Y., has recently compared conservative efforts to defund Obamacare to kamikaze pilots and Gen. George Custer.
Thursday, he called the effort "fraud."
"There's a wing within our party led by people like (Sen.) Ted Cruz, who have been really, as far as I'm concerned, carrying out a fraud with the people" by saying the strategy will work, King
said Thursday on CNN's "The Situation Room."
Cruz, R-Texas, has been leading the defund effort along with Sen. Rand Paul, R-Ky., and Sen. Mike Lee, R-Utah. More moderate members of the GOP say the effort will only hurt the Republican Party. They fear a government shutdown like in the 1990s when Republicans got the blame.
House Speaker John Boehner gave in to demands to tie the vote to raising the debt ceiling.
That vote is set for Friday, with the bill then moving to the Senate. King says the vote can't pass in the Senate, which doesn't have enough Republican votes, and President Barack Obama would veto it anyway.
After an expected Senate vote next week, it will be time for Cruz, Paul, and Lee to "put up or shut up," King said.
"If anything good comes from all of this, when Ted Cruz and Rand Paul and Mike Lee fail in the Senate next week, maybe finally we Republicans will have ended their influence," he said. "We as House Republicans should stop letting Ted Cruz set our agenda for us. He should stay in the Senate and should keep quiet. If he can deliver on this, fine. If he can't, then he should keep quiet from now on, and we shouldn't listen to him."