“One of the first things Congress will do when we finish this debate, I would say give it 60 days, we will pass that extension” on sanctions, Mr. Corker told reporters after a briefing with Energy Secretary Ernest J. Moniz.

But additional options could be in the offing. They include a stand-alone measure to provide more support to Israel, a provision that would approve the use of military force in the region and perhaps a resolution to approve, rather than disapprove, the Iran accord, which could peel away more Democratic support. The House and Senate also are working to reconcile each chamber’s defense bill, which could be a vehicle for these or other options.

At the same time, many Republicans and Democrats are working to assure that several components of the deal hold up.

Senator Chris Coons, Democrat of Delaware, wrote a letter to Mr. Obama in consultation with several other Democrats expressing concerns about the security of Israel, the role of Europe in maintaining sanctions going forward, assurances that Iran would not be able to spend its new pile of cash on supporting terrorism and monitoring of Iran’s nuclear energy.