Senate Foreign Relations Committee Chairman Bob Corker, a Republican, faces challenges this week on the Senate floor to his bipartisan bill that would let Congress weigh in on a potential international nuclear deal with Iran.
Several Republican senators have filed amendments to the bill, which threatens to undermine bipartisan support for the measure.
Republican Senator Marco Rubio, who has announced that he is running for president in 2016, wants to require Tehran to recognize the state of Israel.
Republican Senator John Barraso wants to make the Obama adminstration certify that Iran is not directly supporting any terrorist actions against Americans.
Another amendment would give any final nuclear deal - scheduled to be reached by the end of June - the status of a treaty, which would require ratification by two-thirds of the Senate. Another would require the release of American citizens detained in Iran as part of an agreement.
A number of Democratic and Republican lawmakers have called these amendments "poison pills," which could derail bipartisan support for the Corker bill.
It passed unanimously out of the Senate Foreign Relations Committee.
On the Senate floor Monday, Corker cautioned his colleagues that if the bipartisan bill fails to pass, the Senate will have no say whatsoever on a final nuclear deal the Obama administrations hopes will be reached in the international talks with Iran.
Democratic Senator Tim Kaine also urged the Senate to stay focused on a bipartisan approach, saying Congress has a constitutional duty to weigh in on an agreement as momentous as a potential Iran nuclear deal. The Senate is expected to vote on the Corker bill this week, and it is not yet clear how many amendments will come to the floor for a vote.
An interim agreement reached between Iran and six major world powers would set up an international inspection regime and limit Iran's enrichment of uranium, in exchange for a lifting of economic sanctions against Iran. Negotiators have until the end of June to reach a final, formal accord.
If an accord is reached, the bill would give Congress the chance to review the agreement, and freeze the president's ability to lift sanctions on Iran until the review is complete.