The Senate Foreign Relations Committee unanimously declined on Tuesday, at a critical juncture, to advance legislation that would have overtly threatened ongoing multilateral nuclear negotiations with Iran.

But the panel’s decision to not advance a bill that would have made US diplomats’ work effectively impossible will be challenged by floor amendments, conservative senators warned at a hearing Tuesday.

The committee had agreed to strip out measures that would have made the so-called P5+1 deal contingent on issues not directly related to Tehran’s nuclear program—proposed legislative language that had previously been met by the White House with a veto threat.

The deal–hammered out in the past few days by Senate Foreign Relations Committee Chair Bob Corker (R-Tenn.), its newly appointed ranking member Ben Cardin (D-Md.) and the federally-indicted former ranking member Bob Menendez (D-N.J.)–led the White House to dramatically declare about an hour before the hearing was scheduled to start that it would consider supporting the bill.

“The president would be willing to sign the proposed compromise that is working its way through the committee today,” Josh Earnest, the White House press secretary, said Tuesday afternoon.

That balance, however, is under threat, with right-wing lawmakers hoping to weigh down the process with amendments—52 had been filed prior to the mark-up of the narrowed manager’s package.

“This is an issue we’re gonna have to talk about on the floor as we move forward beyond this place today,” Sen. Marco Rubio (R-Fla.) said, of a provision that would have hinged the deal on Iran recognizing Israel.

Sen. Ron Johnson (R-Wis.), who decried the so-called Corker-Menendez legislation for not forcing the White House to obtain an affirmative senate supermajority before temporarily lifting nuclear sanctions on Iran, alluded to “a number of amendments to provide clarity” that he would withhold for the time being.

He described the legislation, which he nonetheless voted to advance, as giving Congress “an incredibly limited role” that doesn’t allow the senate to provide the executive branch “advice and consent.”

The only amendment offered in committee, a measure brought forth by Sen. John Barrasso (R-Wyo.), would have forced the administration to certify that Iran isn’t a state sponsor of terror as a condition to the deal. It failed 13-6, with the backing of Presidential candidates Sens. Rand Paul (R-Ky.) and Marco Rubio (R-Fla.).

Whether the pair will, on the floor of the Senate, use the measure and their ambitions to complicate the nuclear agreement, there is no shortage of chances for twists in the plot, considering the extensive list of temporarily shelved amendments and Senate Majority Leader Mitch McConnell’s (R-Ky.) past criticism of the negotiations.

“The administration needs to explain to the Congress and the American people why an interim agreement should result in reduced pressure on the world’s leading state sponsor of terror,” the top Republican in the Senate said last week.

Polls taken since that statement was issued could impact McConnell’s calculus on what amendments to allow, however. A Quinnipiac University survery showed, according to a Monday release, that voters in three swing states—Iowa, Colorado, and Virginia–approve of Iran trading nuclear capabilities for sanctions relief by a 3:1 margin. In none of the states did President Obama have a net approval rating, the same research discovered.

“The alternative to this negotiation, this ongoing negotiation, is frightening to the American people,” Sen. Barbara Boxer (D-Calif.) said. “They don’t want another war.”

She vowed to use “every tool at my disposal” to maintain the agreement struck by the committee.

Perhaps reflecting the veracity of Boxer’s declaration is the fact that the key architect of the accord, as chairman-elect, once suggested advancing legislation that would withdraw the administration’s mandate to offer temporary sanctions relief—a feature of the prior nuclear sanctions language passed by congress that serves as a key plank to the multilateral talks with Iran.

“We could do away with the national security waivers… so they would have to come back to us for approval,” Corker said in December.

On Tuesday, however, he was laudatory of the legislative branch’s role to this point, in bringing Iran to the table, and said that “Congress prevailed” over the Obama administration’s desire to see zero additional legislative proposals on negotiations, with a deal not set to be finalized until the end of June.

Democrats, however, cast that analysis into disrepute with their takes on the dynamics between the White House and unanimous approval.

“Congress will be involved,” Sen. Tim Kaine (D-Va.) said. “This only question is will that involvement be helpful and orderly or will it be under free-for-all rules.”

“We have heard very clearly that the changes that have been made over the past 24 to 48 hours essentially make this legislation benign, as it relates to the negotiations,” Sen. Chris Murphy (D-Conn.) also remarked.