WASHINGTON, DC - SEPTEMBER 27: U.S. Senator Ted Cruz (R-TX) (C), Senator Mike Lee (R-UT) (R), and Senator Marco Rubio (R-FL) (L) speak to members of the media after a vote on the Senate floor September 27, 2013 on Capitol Hill in Washington, DC. The Senate has passed a continuing resolution 54-44 to fund the government through November 15 with the exclusion of defunding the Obama care in which the provision was passed in the House.National Journal

Three rebellious foreign policy hawks pushed for a tougher Iran bill. In the end, two of them—both with 2016 hopes—gave in to the overwhelming consensus in the chamber.

The Senate easily passed legislation Thursday that hands Congress a formal review of any U.S.-Iran agreement to limit the Iranian nuclear program in exchange for relief from sanctions.

GOP Sens. Marco Rubio and Ted Cruz, and maverick freshman upstart Tom Cotton, had pushed to make the bill stronger. But even though they were denied the chance for votes on their amendments, Rubio and Cruz ultimately agreed with the Senate consensus as the bill passed 98-1, with only Cotton voting against it.

The White House has indicated that President Obama would sign the bill, backing off an earlier veto threat after Senate Foreign Relations Committee Chairman Bob Corker and Ben Cardin, the panel's top Democrat, negotiated changes that softened the measure somewhat.

Rubio, just before the vote, announced his support for the bill even though he was denied votes on amendments including a plan to make any deal contingent on Iran recognizing Israel's right to exist.

The Florida Republican criticized the lack of amendment votes but said that in the end, it's important to provide a role for Congress in reviewing the potential deal that he believes will likely be too favorable to Iran.

"I hope this bill passes here today so at least we'll have a chance to weigh in on an issue of critical importance," Rubio said. "I think we are better off if we have this process in place," he said.

Cruz's support for the bill was more surprising. It came moments after he voted against a procedural measure to end debate, and one day after he strongly criticized the legislation.

Cruz argued that the bill was too weak absent his amendment to ensure that relief from statutory sanctions could only occur if there's an affirmative vote by Congress to allow it. In contrast, the bill would only provide Congress a chance to vote to disapprove relief from sanctions.

"Don't have a fig-leaf vote and let the President's bad deal go into effect that undermines our national security. Have a meaningful vote that requires the affirmative approval of Congress," Cruz said on the floor Wednesday.

Cruz criticized the bill again Thursday in a statement as a "missed opportunity," while explaining his two votes.

"I voted no on cloture because we should have insisted on amendments to put real teeth in this bill," Cruz said. "Ultimately, I voted yes on final passage because it may delay, slightly, President Obama's ability to lift the Iran sanctions and it ensures we will have a Congressional debate on the merits of the Iran deal."

Cotton also defended his vote in a statement. His opposition comes after he led 46 other Republicans in a controversial letter in March to Iran's leaders that was aimed at undermining the potential deal that the Obama administration is negotiating with the Iranian regime.

"A nuclear-arms agreement with any adversary—especially the terror-sponsoring, Islamist Iranian regime—should be submitted as a treaty and obtain a two-thirds majority vote in the Senate as required by the Constitution," Cotton said. "President Obama wants to reverse this rule, requiring opponents to get a two-thirds vote to stop his dangerous deal. But Congress should not accept this usurpation, nor allow the president any grounds to claim that Congress blessed his nuclear deal."

But in the end, Republicans agreed with the bill that provides oversight, more information for lawmakers, and at least an avenue—however unlikely to muster a veto-proof majority—to try and block the potential agreement that many GOP lawmakers contend will be a bad deal.

All four of the Senate GOP 2016 candidates—Rubio, Cruz, Rand Paul, and Lindsey Graham—were cosponsors of the initial version of the bill introduced in late February by Corker and Democrat Robert Menendez, then the Foreign Relations panel's top Democrat.

House Republicans plan to bring up the bill soon. Speaker John Boehner called it "important, bipartisan legislation" right after the Senate approved it, saying in a statement that, "our goal is to stop a bad agreement that could pave the way to a nuclear-armed Iran."

"I look forward to House passage of this bill to hold President Obama's administration accountable," he said.

Alex Rogers contributed to this article

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