A leading Republican critic of the negotiations, Senator Mark S. Kirk of Illinois, added, “Congress will not permit the president to unilaterally unravel Iran sanctions that passed the Senate in a 99 to 0 vote,” a reference to the vote in 2010 that imposed what have become the toughest set of sanctions.

Such declarations have the Obama administration concerned. And they are a reminder that for a deal to be struck with Iran, Mr. Obama must navigate not one negotiation, but three.

The first is between Mr. Obama’s negotiators and the team led by Mohammad Javad Zarif, the savvy Iranian foreign minister. The second is between Mr. Zarif and forces in Tehran that see no advantage in striking a deal, led by many in the Iranian Revolutionary Guard Corps and many of the mullahs. The critical player in that effort is Ayatollah Ali Khamenei, who has reissued specific benchmarks for an accord, including Iran’s eventual expansion of its uranium enrichment program by nearly tenfold. And the third is between Mr. Obama and Congress.

Mr. Zarif, in an interview last summer, said that Mr. Obama “has a harder job” convincing Congress than he will have selling a deal in Tehran. That may be bluster, but it may not be entirely wrong.

Many of the details of the negotiations remain cloaked. The lead negotiator, Wendy Sherman, the under secretary of state for political affairs and a leading candidate to become the State Department’s No. 2 official next month, struck a deal with congressional leaders that enables her to avoid public testimony when the negotiations are underway. Instead, she conducts classified briefings for the key congressional committees.

But it is clear that along with the fate of Iran’s biggest nuclear sites — Natanz and Fordow, where uranium fuel is enriched, and a heavy-water reactor at Arak that many fear will be able to produce weapons-grade plutonium — the negotiations have focused intently on how sanctions would be suspended. To the Americans, the sanctions are their greatest leverage. For many ordinary Iranians, they are what this negotiation is all about: a chance to boost the economy, reconnect with the world and end Iran’s status as a pariah state.

For that reason, many think Mr. Obama’s best option is to keep the negotiations going if a deal is not reached by the deadline, a possibility both Iranian and Russian officials have floated.