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House Republicans, in an unusually caustic intra-party squabble, are ripping their conservative colleagues in the Senate for what they see as an abrupt cave-in on the push to de-fund ObamaCare.

“They're waving the white flag already,"one House GOP lawmaker said Wednesday.

The squabble started after House Speaker John Boehner earlier in the day announced he would agree to the demands of Tea Party-aligned lawmakers to tie a vote on de-funding the health care law to a vote on a must-pass budget bill.

The move would effectively condition the approval of the spending bill on ObamaCare being de-funded, or else risk a government shutdown when funding runs out at the end of the month.

But Sen. Ted Cruz, R-Texas, one of the most vocal supporters of the “de-fund ObamaCare” push, startled his House colleagues when he released a written statement Wednesday afternoon that appeared to acknowledge the bill will probably fail in the Senate.

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    “Today's announcement that the House will vote to defund ObamaCare is terrific news,” Cruz said, in a press release from him, Sen. Marco Rubio, R-Fla., and Sen. Mike Lee, R-Utah.

    “Harry Reid will no doubt try to strip the defund language from the continuing resolution, and right now he likely has the votes to do so. At that point, House Republicans must stand firm, hold their ground, and continue to listen to the American people.”

    House Republicans are concerned that this kind of approach effectively pins the entire effort on the House.

    "We expect them to stand and filibuster like Rand Paul," fumed one senior House GOP aide.

    "It's time to put on the big boy pants," said one House Republican who didn't want to be identified. "Maybe this will wean us of the bed-wetters."

    A senior GOP leadership aide said they don't expect this dissension to blow up the bill in the House on Friday. But they are concerned about where things are going now if the GOP senators don't defend their turf.

    Effectively, in announcing the new bill, Boehner and his deputies backed off a compromise approach they earlier tried to sell to rank-and-file conservatives. Under that plan, the House would have sent two bills to the Senate -- one to de-fund ObamaCare, the other to fund the government. The Senate, then, would have been able to easily bypass the ObamaCare bill and send the spending measure straight to the White House, in turn averting a government shutdown.

    But House conservatives revolted, and Boehner now is tying the two votes together.

    But the plan is undoubtedly risky.

    Both Obama and Senate Democratic Leader Harry Reid have suggested Republicans will bear the brunt of the blame if the gambit results in a government shutdown.

    Obama blasted Republicans during an interview Tuesday with Telemundo.

    "We're hearing that a certain faction of Republicans, in the House of Representatives in particular are arguing for government shutdown or even a default for the United States of America ... if they don't get 100 percent of what they want," Obama said.

    Current funding for the government is set to expire at the end of the month, and lawmakers must approve the stopgap bill in order to keep Washington open.

    The GOP measure would fund the government through Dec. 15, at current funding levels. Republicans also plan to push a measure dealing with the debt ceiling, with a mid-October deadline looming for when the government can no longer honor its obligations.

    Fox News' Chad Pergram contributed to this report.