Partisans in the debate over a Senate bill that would threaten onerous new antinuclear sanctions on Iran escalated their lobbying on Tuesday, with critics submitting a letter to lawmakers signed by 62 multifaith organizations urging a delay and supporters pointing to what they called Iran’s insincerity.

President Obama has said the bill, which already has strong bipartisan backing in the Senate, could sabotage the administration’s efforts to negotiate a comprehensive agreement with Iran that would ensure its nuclear activities are peaceful, resolving a prolonged dispute that has raised the possibility of another armed conflict in the Middle East.

Mr. Obama has threatened a veto, but the bill may already have enough support to potentially override that, and it is unclear how long the administration can delay a vote.

The bill, co-sponsored by Senator Mark S. Kirk, an Illinois Republican, and Senator Robert Menendez, a New Jersey Democrat, has acquired added significance in recent days because of a temporary agreement in the nuclear negotiations that will freeze parts of Iran’s nuclear activities for six months in return for a partial easing of economic sanctions that have been imposed by the United States and the European Union.