Washington (CNN) A top State Department official warned Monday that the White House could revive its veto threat of a Senate bill on Iran if certain amendments under consideration get added to the measure.

"There will be a lot of pretty awful amendments quite frankly," Wendy Sherman, undersecretary of state for political affairs, said of the legislation, which is expected to go to the floor for a vote this week. "And we'll see where we end up."

President Barack Obama withdrew his initial veto threat after Republican Sen. Bob Corker of Tennessee and Democratic Sen. Ben Cardin of Maryland eliminated several provisions the administration disliked from a compromise version of the bill that, which the amendments certain Republicans are proposing threaten to upend.

But Obama's support for the legislation, which would give Congress the ability to weigh in on a final nuclear deal with Iran, only holds if it does not undergo any radical changes, Sherman emphasized.

"The president has said that if the Corker-Cardin legislation stays where it is, he will not veto it," Sherman said. "If it becomes something else, then he'll have to consider his options."

As of Monday afternoon, there were 23 amendments to the bill offered by a half dozen GOP senators, with more expected. Democrats have indicated they probably will not propose any changes.

Florida Sen. Marco Rubio, who is seeking the 2016 GOP presidential nomination, is looking to add an amendment requiring Iran's leaders to publicly acknowledged Israel's right to exist. Such a statement is anathema to Tehran.

Another Republican presidential candidate, Sen. Ted Cruz of Texas, wants Congress to have a straight up or down vote on the deal. "It is imperative that, at the very least, the President obtain majority support for this deal from both Houses of Congress before moving forward," Cruz said.

The office of Kentucky Republican Sen. Rand Paul, also a presidential contender, would not say if he would offer changes.

Other amendments that could draw scrutiny from the President include proposals to require Iran to renounce terrorism, certify that it has not participated in terrorism, release several Americans imprisoned in Iran and allow nuclear inspections anywhere, anytime, including at Iran's military facilities.

Similar amendments were floated when the bill was considered by the Foreign Relations Committee but most were dropped in order to preserve the President's support.

"Any deal along the lines the President proposed two weeks ago is dangerous for the United States and dangerous for the world, and it is Congress's job to stop such a deal before it happens," said Sen. Tom Cotton of Arkansas, a vocal freshman Republican opponent of the bill who plans to offer several amendments this week. "They are good amendments that would strengthen this bill."

Corker and other supporters of the legislation, however, said they would try to fend off major changes so the thrust of what came out of committee remains intact.

"As we deal with this legislation on the floor, I believe there are enough people in the Senate who understand that a degree of balance must be maintained to ensure this bill becomes law," Corker said.

"I will oppose amendments -- at least with my own vote -- that I consider to be poisonous and undermine the very essence of what we accomplished in the Senate Foreign Relations Committee," said New Jersey Democratic Sen. Robert Menendez, an early sponsor of the legislation.

Aides in each party said they were unsure if any of the amendments would be approved. A 60 vote threshold is likely for them to pass. Democrats said they were hopeful enough senators would stand against major changes, but GOP aides were less certain.

Voting could begin as early as Tuesday with a final vote on the bill possible by Thursday, according to GOP aides.

Sherman was addressing a crowd from the Religious Action Center of Reform Judaism, a Jewish-American interest group that is generally supportive of ongoing negotiations with Iran even as it has expressed concerns about the trustworthiness of Iran's government.

In her remarks, Sherman emphasized the administration's commitment to reaching a verifiable deal with Iran while also maintaining Obama's "unwavering commitment to Israel's security."

She further refuted the notion some critics have put forward that removing harsh sanctions on Iran would empower the country to pursue its nuclear program without consequence.

"The sanctions that we have on Iran, which are U.S. sanctions, E.U. sanctions, U.N. Security Council sanctions, are quite vast and quite effective," Sherman said. "But they are not effective at preventing Iran from having a nuclear weapon."

Sherman noted that Iran increased the number of centrifuges it has from 164 to 19,000 under the current sanctions regime.

Furthermore, she emphasized that the sanctions regime could crumble if the U.S. is seen as walking away from the talks.

"Countries around the world, even good allies like Japan and South Korea, were willing to limit the amount of oil they imported from Iran because they believed we were working towards a peaceful solution," she said. "If they feel we aren't working towards a peaceful solution, they are likely to break ranks and we won't be able to keep the sanctions together anyway."

Sherman, who recently returned from the latest round of nuclear negotiations with Iran in Vienna, said the administration is ready to work "non-stop" until the end-of-June deadline for a final agreement.

Secretary of State John Kerry is set to meet with his counterpart, Iranian Foreign Minister Mohammad Javad Zarif, on the sidelines of a U.N. conference Monday in New York.