This week, the US and Iran laid out a framework for the broad strokes of a deal to limit Iran's nuclear program. But now, members of Congress are trying to weigh in — and potentially kill it. Can they?

A proposed bill from Sen. Bob Corker (R-TN) would create a path to block Obama from carrying out a key feature of any eventual agreement — lifting the Congressional sanctions on Iran — if veto-proof supermajorities in each chamber voted to disapprove the deal.

But Republicans can't pass it on their own. To override Obama's promised veto, they'll need 13 Democrats in the Senate — and more than 40 in the House. And though some Democrats are already on board, and have been willing to sign onto "tough on Iran" measures in the past — it's not yet clear that they'll back this one if a deal that looks good to them is in sight.

The bill that could scuttle a deal

Right now, Obama doesn't need Congress to lift the vast majority of US sanctions on Iran. He can do it mainly through the Treasury Department.

That's what Republicans in Congress want to change. Corker, the chair of the Senate Foreign Relations Committee, is pushing the Bipartisan Iran Nuclear Agreement Review Act of 2015. This bill would first delay, and then potentially, eliminate the administration's power to lift many of these sanctions.

That means the bill would, effectively, let Congress disapprove any deal with Iran. For 60 days after an agreement is finalized, "the president is prohibited from suspending, waiving or otherwise reducing congressional sanctions," the bill's sponsors say.

That two-month period gives Congress a chance to weigh in. If the legislature does nothing or votes to approve the agreement, Obama can start lifting the sanctions. But if both houses of Congress pass a resolution of disapproval with veto-proof majorities, Obama would be stripped of his authority to relieve those sanctions — which would mean the deal would be scuttled.

So Corker's bill wouldn't technically kill any deal, and indeed, he is arguing that it would merely give Congress a say in the matter. But it would let a congressional supermajority have the chance to block Obama from carrying out a key component of any agreement.

Can Corker's bill beat Obama's veto?

Since Obama has pledged to veto Corker's bill, two-thirds of both the House and Senate would need to back it to make it law. Then, if a deal with Iran is finalized and actually considered, another veto-proof majority would be needed to disapprove it.

Strong Republican support for the Corker bill is almost certain, especially with many GOP senators and House members already on record opposing any agreement that would allow Iran to continue any enrichment — as the current framework does. Sen. John Thune (R-SD), a member of the GOP leadership, told the Washington Post that "since this deal allows them to keep centrifuges and continue to enrich in some circumstances, those kind of particulars are going to be tough for most Republicans to handle or be for."

But Republicans won't be enough. To override Obama's veto, the bill would need two-thirds support in each chamber. Assuming unanimous GOP support, that means 13 votes from the Senate Democratic caucus and 46 from House Democrats.

In the Senate, nine Democrats have already signed on as cosponsors (including Sen. Angus King of Maine, who is technically an independent caucusing with Democrats), with several more supporters said to be waiting in the wings.

But the dynamics may change now that a framework for a deal is in hand. Politico's Burgess Everett is already reporting that some senators are now qualifying their past support for Corker's bill. "I'm not in if it's a partisan weapon," Sen. King told Everett.

The new acting top Democrat on the Senate Foreign Relations Committee, Ben Cardin (D-MD), has also been cautious. Though he has supported toughening sanctions on Iran in the past, Cardin told Everett that "a review process established by Congress makes sense," but "I want it to strengthen the president, not weaken the president." Cardin has temporarily taken the lead spot on the committee after the indictment of Sen. Bob Menendez (D-NJ), a strong supporter of Corker's bill.

The most important Democratic supporter of Corker's bill is probably Sen. Chuck Schumer (D-NY) — Senate Democrats' leader-in-waiting. Schumer has long supported tough-on-Iran measures, and backed this bill just weeks ago. Now, though, he's under heavy pressure from the White House to back down — or at least not to push for the bill too strongly. Politico's Manu Raju and John Bresnahan write that Hill insiders think strong Schumer support would give other Democrats "the political cover to break with Obama on the issue."

The situation in the House is less clear. Though huge supermajorities in the chamber have regularly signed on to letters calling for a hard line in negotiations, it's not evident what Democrats will do if presented with a deal that the administration argues strenuously is a good one. The White House is arguing that Corker's bill encroaches on the president's authority to conduct foreign policy. And even if the bill passes, another veto-proof supermajority in each chamber would be necessary to actually disapprove any final agreement with Iran.

Corker's bill will be considered by the Foreign Relations Committee on April 14, so we'll get a better sense of things then. If Democrats start to buy into Obama's argument that the emerging potential agreement is a good one — and start to view Corker's proposal as a partisan effort to undermine it — they may back off their past support. But if not — if they keep arguing that the bill would merely give Congress a voice — the administration may face some trouble ahead.