“There’s a bit of a sense of desperation about coming up with ways to break the logjams, on the nuclear talks and the larger relationship,” another participant in the negotiations said. “Because if we don’t figure this out in the next few months, it is not clear the opportunity is going to come again.”

The Iranians are clearly doing far better in public diplomacy in New York than are the United States or its allies. Mr. Zarif, who is American-educated, media savvy, and often humorous, has already given interviews to the radio network NPR, parried with members of the Council on Foreign Relations in an on-the-record meeting, and made Iran’s case in background briefings.

While he has taken many pokes at President Obama for being slow to confront the Islamic State, he has also mocked the conspiracy theorists in Tehran who claim the Sunni group was invented by the C.I.A.

By contrast, the Obama administration has rarely allowed its negotiating counterparts to Mr. Zarif to go on the record; after the first full day of talks, the officials spoke to reporters only on background, meaning their names could not be used. They complain that Mr. Zarif talks a good game, but has offered few meaningful cuts in the centrifuges. Both sides are clearly worried, because if they cannot win agreement on the main issue over the next 10 days or so — how much fuel-production ability Iran will be allowed to maintain, and how long an agreement to limit its production abilities will last — it is hard to imagine how the complex details of a final accord can be resolved in the remaining time. Which is where the plumbing comes in.

Disconnecting the pipes is one of several ideas that have emerged from the conversations between Mr. Obama’s negotiating team and the Energy Department’s national laboratories, which develop and maintain the American arsenal of nuclear weapons.

But the proposal is not without flaws. “To be credible, it would have to keep the Iranians from restoring operations for a considerable period of time,” said Robert Einhorn, a former member of the negotiating team who is now at the Brookings Institution.