(CNN) After months of tensions with Congress over a bill giving the legislature a say in the potential Iran nuclear deal, the White House indicated Tuesday that the president would be willing to sign the compromise version of the measure.

The Senate Foreign Relations Committee unanimously approved the new version, which Democratic lobbying had watered down, in a vote Tuesday afternoon.

During his daily press briefing, White House press secretary Josh Earnest said President Barack Obama would approve the measure as it stands now, though Earnest noted he can't commit to that position if the legislation changes.

The White House "certainly" blinked, Arizona Republican Sen. Jeff Flake said Tuesday on CNN's "The Situation Room."

"Congress imposed the sanctions and only Congress can lift them permanently. So we always had a role and I'm glad the White House recognizes that now," he said.

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Earlier Tuesday, the top Republican and Democrat on the Senate Foreign Relations Committee said they had resolved key differences on the bill regarding Iran's nuclear plan, making the bill's passage more certain.

"What I'm most proud of is we've kept the pure integrity of the process in place and the President cannot lift -- while Congress is reviewing this -- cannot lift the congressionally mandated sanctions, which is what they've been trying to do and push for over the past couple of weeks," Senate Foreign Relations Committee Chairman Bob Corker told reporters Tuesday, as he headed into a classified briefing on the emerging Iran agreement with Secretary of State John Kerry and other top administration officials.

Florida Republican Sen. Marco Rubio said during the committee's deliberations in the afternoon that he would not offer a controversial amendment related to Israel. Other senators also dropped their amendments to ensure this agreement stayed intact.

According to a Corker aide familiar with the details of the bill, it requires Obama to submit the final agreement to Congress, which will have up to 52 days to weigh in on the deal. That includes an initial review period of 30 days, with 12 more days added automatically if Congress passes a bill and sends it to the President, and an additional 10 days of congressional review if Obama vetoes the legislation.

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If the deal is submitted late, after July 9, the review period reverts to 60 days.

During that time, the President is prohibited from waiving the congressional sanctions. And Obama is required by the legislation to certify to Congress every 90 days that Iran is complying with the terms of the deal.

The bill also requires the President to make a series of detailed reports to Congress on a range of issues, including Iran's nuclear program, its ballistic missiles work and its support for terrorism globally, particularly against the U.S. and its allies.

Sen. Ben Cardin, the committee's top Democrat, expressed optimism Monday night that negotiators could come to an agreement that would appease the White House while maintaining the ultimate goal of requiring congressional approval.

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"I think we can get to a place where we can deal with most of the White House's concerns and maintain the purpose of the bill, which is an orderly congressional review and timely notice if there are material breaches," he said ahead of the compromise being reached.

Congressional negotiators worked through the weekend and into the night Monday to hammer out legislation that would draw enough support from hardline Republicans and moderate Democrats to pass.

House Speaker John Boehner on Tuesday said he expected the House to take up the Corker bill once the full Senate votes on it, saying the proposal has taken "center stage."

He reiterated his stance that Congress should "absolutely have the opportunity to review the deal," adding the administration "appears to want a deal at any cost."

But he brushed off the notion that he was working to derail the nuclear deal.