The compromise legislation, which would allow Congress to review a nuclear accord and potentially reject it, has already survived one test, passing committee on a surprising 19-0 vote after sponsor Sen. Bob Corker (R-Tenn.) offered concessions to Democrats. But opponents say the administration has been too soft on Tehran, and they’re prepping another salvo that could scuttle the measure when it hits the floor this week.

Rubio (R-Fla.) wants to require Iran to recognize the state of Israel. Wyoming Republican John Barrasso wants to make the administration certify that Iran is not directly supporting terrorists’ actions against Americans. Both amendments could damage ongoing talks with Tehran, in the eyes of the White House, because they are seen as outside the scope of the nuclear negotiations. The administration lobbied hard against them when the bill was in committee, and their passage would revive Obama’s veto threat.

That’s not going to dissuade Rubio, who said he would “absolutely” press for floor votes on some of his amendments, a list that also includes a provision requiring the release of Americans imprisoned in Iran, such as Washington Post reporter Jason Rezaian.

“I’m certainly very concerned about people being held in Iran,” Rubio added. Other poison pills could emerge on the freewheeling Senate floor, where any of the 100 members could try and take aim at the measure, and several lawmakers, including Sen. Tom Cotton (R-Ark.), want less to review the Iran deal than to kill the whole thing.

Republican and Democratic leaders, who back the review bill, plan to muster enough votes to block any seriously problematic amendments while still allowing their members to take some political potshots. If they let through any bombshells that significantly undermine the White House’s negotiations, they risk losing Democratic support and the veto-proof majority that Corker has painstakingly assembled. Leaders and members of the Foreign Relations Committee are angling for a bipartisan show of force to reject any major changes, according to interviews with senators and aides close to the strategy, yet another sign that lawmakers in both parties want to make sure their voices are heard on the nuclear deal.

“We need to keep the number of bipartisan supporters for the bill. So that will be the primary goal,” said Senate Majority Whip John Cornyn (R-Texas). “That’s the key to it,” said Minority Whip Dick Durbin (D-Ill). It “can all go awry on the floor. So we’ve got to fight off bad amendments.”

Corker, the gregarious, deal-cutting chairman of the Foreign Relations Committee, has already written and rewritten the measure to win votes from Democrats on the panel without losing GOP support. The bill would allow Congress to vote against removing legislative sanctions if Congress disapproves of a final nuclear deal with Iran, and it would require this administration and future ones to certify that Tehran is following any nuclear deal’s parameters.

On Wednesday, in a private party lunch, Corker made a forceful pitch to the entire 54-member GOP caucus with a relatively simple assertion: His bill is much better than the alternative, which is no congressional say at all on the controversial negotiations with Iran. Because Obama views any bill as an infringement on his presidential negotiating prerogatives, supporters of the legislation have known all along they need a veto-proof majority.

“I just talked about the virtues about it,” Corker said in an interview. “We’re in a situation now where Congress has absolutely zero input.” He added: “It’s pretty strong.”

Still, Corker admits things may be out of his hands when the legislation hits the Wild West of the Senate floor. As written, Corker believes, it’s tough enough for Republicans while still being sufficiently deferential to the president and his Democratic allies in Congress, so Obama can finish his final negotiations with Iranian leaders and world powers over the next two months. Corker has spoken to House Speaker John Boehner (R-Ohio), who plans to take up the bill once it passes the Senate.

But Corker declined to predict exactly how this week’s action on the floor will go. “I want to make sure it passes in a form where it can become law,” Corker said. “I have no idea what some of the amendments are; there may be some improvements that I may not be aware of. We’ll see which ones really need a vote.” In a chamber where senators blundered into six weeks of painful bickering over a human trafficking bill that enjoyed unanimous support, it pays to be wary of the unexpected.

Sen. Ron Johnson (R-Wis.) is insistent that he will make the Senate vote on an amendment that would require the Iran deal to be treated more like a treaty, thus requiring two-thirds approval from the Senate for the nuclear pact to be approved. Johnson withheld his amendment in committee, but he’s ready to move on it on the floor.

Democrats, on the other hand, are being discouraged by party leaders from offering amendments that could throw the measure out of balance. “I have not heard of a single amendment on the Democratic side,” said Foreign Relations ranking member Ben Cardin (D-Md.), who has worked closely with Corker to keep Democrats on board.

At the same time, Republican leaders and Corker himself say that there’s little chance of avoiding some tough votes.

Johnson said his intention is to clarify “what this is and what this isn’t.” And his effort is gaining steam in the hawkish wings of his party.

“Ron Johnson is right that it upends the constitutional framework,” said Cotton. “A major arms control treaty with the world’s leading state sponsor of terrorism should be treated as a treaty.”

Though Johnson’s amendment will amount to a tough vote for nearly everyone in the Senate, supporters of Corker’s bill are confident they can reject it. “That ain’t going anywhere. Everybody knows that’s a poison pill, much as I’d like to see that,” said Sen. Jim Risch (R-Idaho).

Other amendments, like the Iranian prisoners provision, could be incorporated into the bill in a noncontroversial manner. It could be included as a nonbinding “sense of the Senate” provision. In fact, nonbinding language may be the solution for soothing those who want the bill to reflect all of the Senate’s endless grievances with the Iranian government.

“It depends on how you do it,” Cardin said. “On any of the substantive provisions, we’re going to limit it.”

Members of the Foreign Relations Committee may have to ride herd on the floor. In the committee, Barrasso’s amendment to restore terrorism certification requirements was rejected 13-6, with some senators who support that requirement in principle voting against because its addition could imperil the overall bill.

The dynamic has put some Republican senators in an unusual position: urging their colleagues not to force amendment votes, a 180-degree turn from the GOP’s time in the minority, when its inability to get votes on its proposals created a bitterly partisan atmosphere that rarely translated into bipartisan cooperation.

“I would love to send a clean bill to the House. I really would. This is not the place to put a lot of amendments,” said freshman GOP Sen. David Perdue of Georgia. “We got what we wanted, which is a right to look at this deal.”

And for those who say Congress needs a stricter bill that may upend what may be a whopping Senate victory, Sen. Lindsey Graham (R-S.C.) has a message: You’re only helping Tehran.

“Anybody who offers an amendment that will break this agreement apart,” Graham said, “the beneficiary will be the Iranians.”