Republican Sens. Ted CruzRafael (Ted) Edward CruzViral video shows O’Rourke air-drumming to the Who’s ‘Baba O’Riley’ after Cruz debate Five takeaways from Cruz, O'Rourke's fiery first debate NY Times, McCabe give Trump perfect cover to fire Rosenstein, Sessions MORE and Mike LeeMichael (Mike) Shumway LeeEx-college classmate accuses Kavanaugh of sexual misconduct Kavanaugh accuser agrees to testify next week Reexamining presidential power over national monuments MORE said Wednesday that they won't try to block the bipartisan deal to reopen the government and raise the debt ceiling.

"The timing of the vote will make no difference to the outcome," Cruz (Texas) said. "I have no intention of delaying the vote."

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Cruz and Lee (Utah) had spearheaded the campaign to attach ObamaCare language to any new budget bills, and had pushed their colleagues to take a hard-line stance. 

But the pair emerged from a meeting of Senate Republicans Wednesday afternoon to say they would let the budget agreement — which contains only one provision on ObamaCare — move forward.

"Some of us want to see it first — we still don't have text," Lee said. "But provided we get the text and have time to review it and everything, I suspect we'll collapse the time."

There has been speculation that the bipartisan deal might originate in the House, thereby eliminating some procedural hurdles when the bill moved to the Senate. But with Cruz and Lee withdrawing their filibuster threats, several GOP senators said the upper chamber will likely act first on the agreement.

The deal reached by Senate Majority Leader Harry ReidHarry Mason ReidKavanaugh furor intensifies as calls for new testimony grow Dems can’t ‘Bork’ Kavanaugh, and have only themselves to blame Dem senator: Confidential documents would 'strongly bolster' argument against Kavanaugh's nomination MORE (D-Nev.) and Senate Minority Leader Mitch McConnellAddison (Mitch) Mitchell McConnellGrassley: Dems 'withheld information' on new Kavanaugh allegation Kavanaugh accuser set to testify Thursday McConnell told Trump criticism of Kavanaugh accuser isn't helpful: report MORE (R-Ky.) would fund the government through Jan. 15 and raise the debt ceiling until February. It would require income verification for subsidies under ObamaCare, but otherwise leave the healthcare law untouched.

The weeks-long fight over ObamaCare has left the GOP sharply divided and licking its wounds, after centrist Republicans warned for weeks that the battle was futile and damaging to the party.

Several Republicans left the meeting Wednesday grumbling that the conservatives in their ranks had prolonged the impasse even as Republicans were sinking in the polls.

"We left a lot on the table because we couldn't get our act together, but this is the best Mitch could do," said Sen. Lindsey GrahamLindsey Olin GrahamHouse Judiciary chair threatens subpoena if DOJ doesn’t supply McCabe memos by Tuesday Rosenstein report gives GOP new ammo against DOJ Graham: There's a 'bureaucratic coup' taking place against Trump MORE (R-S.C.), who will vote for the deal. "We need to stop the bleeding, lessen the damage to the party."

Sen. John McCainJohn Sidney McCainTrump hits McCain on ObamaCare vote GOP, White House start playing midterm blame game Arizona race becomes Senate GOP’s ‘firewall’ MORE (R-Ariz.) echoed that message.

"I hope it is another 15 years at least before we have to go through this exercise again," McCain said. "We're in a hole, we have to dig out and come up with a positive agenda."

A number of Republicans have emerged in recent days to pressure Cruz to back down from his insistence that ObamaCare be scaled back considerably as part of a budget deal.

"I would hope that whatever comes forward, that we would allow a vote on it as soon as possible," Sen. Kelly AyotteKelly Ann AyotteGOP mulls having outside counsel question Kavanaugh, Ford Pallbearers, speakers announced for McCain's DC memorial service and Capitol ceremony Tributes pour in for John McCain MORE (R-N.H.) told CNN Wednesday morning.

Cruz, for his part, denied that he ever aimed to block the vote.

"I never had any intention to delay this vote," he said. "I thought it was interesting to read in the papers speculation that others were asking me not to delay this vote because no one in Republican leadership ever asked."

Sen. Bob CorkerRobert (Bob) Phillips CorkerPoll: More voters oppose Kavanaugh’s nomination than support it Ford opens door to testifying next week Police arrest nearly two dozen Kavanaugh protesters MORE (R-Tenn.) said he never thought Cruz and others would filibuster the McConnell deal.

"At some point when you've reached the end of the road to then make life miserable for no reason ... then the pendulum swings," Corker said.

Corker said he would not "tout" the deal as a GOP victory but said that it at least preserved the sequester in the Budget Control Act, which he said was perhaps the best thing he had ever voted for.

"I am not going to champion it, all I am going to say is we did not go backwards," he said.

Wednesday's breakthrough follows weeks of high-stakes wrangling between the GOP-controlled House and Democratically controlled Senate over how to fund the government and hike the $16.7 trillion debt ceiling. Treasury Secretary Jack LewJacob (Jack) Joseph LewOvernight Finance: US reaches deal with ZTE | Lawmakers look to block it | Trump blasts Macron, Trudeau ahead of G-7 | Mexico files WTO complaint Obama-era Treasury secretary: Tax law will make bipartisan deficit-reduction talks harder GOP Senate report says Obama officials gave Iran access to US financial system MORE has warned that the government would be unable to pay all of its bills beyond Wednesday if Congress didn't act first.

If the Senate passes the package on Wednesday, as expected, the bill would move to the House, all but forcing Speaker John BoehnerJohn Andrew BoehnerBlue wave poses governing risks for Dems Nancy Pelosi: Will she remain the ‘Face of the Franchise’? Jordan hits campaign trail amid bid for Speaker MORE (R-Ohio) to bring it up for a vote.

With Tea Party conservatives already lining up in opposition, BoehnerJohn Andrew BoehnerBlue wave poses governing risks for Dems Nancy Pelosi: Will she remain the ‘Face of the Franchise’? Jordan hits campaign trail amid bid for Speaker MORE will likely need an overwhelming number of House Democrats to get the package to President Obama.

On the walk from his office to the House chamber on Wednesday at noon, Boehner was silent in the face of questions about the emerging deal..

Erik Wasson, Peter Schroeder, Alex Bolton, Elise Viebeck and Sam Baker contributed.

— This story was last updated at 1:36 p.m.