Sen. Marco Rubio (R-Fla.) is seeking votes on no fewer than seven amendments to the Iran legislation. (Scott Olson/Getty Images)

The Senate’s ambitious young conservatives have the chance this week to demonstrate their ability to lead on the big foreign policy issue of the day as debate begins on legislation that would allow some congressional oversight of a potential nuclear deal with Iran.

But there is also a chance that the presidential ambitions of these same senators could undermine a tenuous agreement that has been in place for two weeks now, reigniting a conflict between the Obama administration and Congress.

Marco Rubio (R-Fla.), Rand Paul (R-Ky.) and Ted Cruz (R-Tex.), three first-term senators running for president after just a couple of years in office, have faced questions about their grasp of, and gravitas on, some of the critical foreign policy questions that have dominated the early stages of the presidential campaign.

That makes this week’s debate on the Iran legislation a chance to showcase their international acumen, but proposals by Rubio, backed by Paul, and one from Cruz could cause Democratic support for the measure to evaporate, undermining a bill carefully drafted by Senate Foreign Relations Committee Chairman Bob Corker (R-Tenn.).

Rubio, a member of Corker’s panel, is seeking votes on no fewer than seven amendments, including a mandate that Iran acknowledge Israel’s “right to exist” and a requirement that Iran release all American prisoners before the nuclear deal would take effect. Cruz has a small but critically important amendment that would tweak the language to require that the nuclear deal receive an affirmative vote of approval in Congress to be cinched.

“It is imperative that, at the very least, the President obtain majority support for his deal from both Houses of Congress before moving forward,” Cruz said in a statement announcing the amendment, which is co-sponsored by Sen. Patrick J. Toomey (R-Pa.).

Corker spent weeks negotiating with Democrats, generating enough momentum that the Obama administration reversed course and agreed to support the legislation.

On Tuesday, Corker began his effort to beat back any amendments that would disrupt the legislation’s path to Obama’s desk, objecting to an amendment from Sen. Ron Johnson (R-Wis.) that he otherwise supported. “Let’s not let the perfect be the enemy of the good,” he said during a floor speech, reciting several aspects of the bill that would be lost if Obama was to veto it. “Let’s ensure that we have the ability to see the details of this bill.”

In a good omen for Corker’s efforts to maintain bipartisan support, the Senate rejected Johnson’s amendment, 57 to 39.

Earlier in the week, Corker noted that Paul and Rubio sit on his committee and “handled themselves, I thought, in a very responsible way” during the bill’s consideration there.

But Democrats are requesting a bipartisan blockade of the amendments, which some in their caucus would otherwise support, to take the political sting out of the vote.

“I’m concerned that they and other others want to use this good, bipartisan piece of legislation as a platform for their political ambitions,” Senate Minority Leader Harry M. Reid (D-Nev.) said Tuesday. “This bill is too important to be a pawn in anyone’s political game.”

The consensus legislation would give Congress 30 days to review a nuclear pact with Iran, during which Obama would be able to waive sanctions against the Tehran regime that were imposed by the executive branch but would have to leave in place those sanctions previously drafted by Congress.

If the House and Senate passed resolutions disapproving of the Iran deal, including overcoming a possible presidential veto, then Obama would be forced to leave in place those congressionally mandated sanctions. Any other outcome, including a deadlock in which the legislation just stalls with no clear outcome, would allow Obama to go ahead implementing all aspects of any nuclear deal.

This last aspect of the legislation was a critical move by Corker to win over Sen. Timothy M. Kaine (D-Va.), who negotiated key aspects of the legislation with the chairman on a trip to the Middle East in January. Kaine helped bring along many other Democrats to support Corker’s plan, which had initially received just tepid bipartisan backing because Democrats did not want to undermine the president.

Now, after a unanimous committee vote, Corker brings his legislation to the Senate floor this week hoping again for a big bipartisan victory without any major alterations to the legislation, or else it could again receive a veto threat.

Joining him are top GOP foreign policy and national security voices who say that it is paramount to establish a congressional review framework for a nuclear deal.

“Anybody that monkeys with this bill is going to run into a buzz saw,” Sen. Lindsey O. Graham (R-S.C.) told reporters last week. “I don’t want to monkey around with this thing to make political points. I want to try to get a process that we can approve a good deal or kill a bad one.”

Graham, who is considering a presidential run of his own, had a sharp message for critics of the compromise hashed out between Corker and Sen. Benjamin L. Cardin (D-Md.), the ranking Democrat on the Foreign Relations Committee: “Most of you haven’t lifted a finger to solve this problem. Most of you haven’t met with one Democrat. So don’t parachute in here at the end with an idea that will destroy what I think is one of the most important pieces of legislation that I’ll ever deal with.”

Sharing Graham’s view was the American Israel Public Affairs Committee, which told senators in a message Tuesday to “bear in mind the need to retain the bipartisan consensus this legislation enjoys” and to “refrain from supporting provisions that could harm that bipartisan support.”

Cruz, Paul and Rubio have all signaled that they would support tougher language in the Corker bill that would make it more difficult for Obama to finalize a deal with Iran.

“In my mind, if the president wanted this to be a permanent deal that survived his presidency, he would have brought it to Congress,” Rubio told NPR earlier this month.

Paul has taken a less publicly aggressive stance on the Iran legislation.

At the bill’s April 14 committee markup, Paul joined Rubio in voting for an unsuccessful amendment that would have toughened anti-terrorism language in the bill. But he was one of only two members of the committee who did not speak on the compromise bill before voting with 18 fellow senators to advance it.

In a Fox News interview after his presidential campaign announcement, Paul said he supported amendments such as Rubio’s that could torpedo Democratic support. But in a subsequent interview on CBS’s “Face the Nation” earlier this month, Paul described himself as “a Republican who does believe in negotiations.”

“I really do want, sincerely want, a deal, and I don’t want war,” he said, while expressing doubts about the trustworthiness of the Iranian regime.