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President Barack Obama has a personal stake in the outcome of Monday's meeting in Vienna between Western and Iranian nuclear experts on the future of Iran's stockpile of low-enriched uranium. That's because, Administration sources tell TIME, Obama personally weighed in three times during secret, multiparty negotiations with the Iranians over the last four months — in what has become not just a test of Iran's nuclear intentions but also a test of Obama's effort to limit Iran's nuclear ambitions through a combination of sanctions, threats and incentives.

The backroom talks began in June, when Iranian officials told the International Atomic Energy Agency their country was running out of fuel for an aging research reactor built for the Shah in 1967 by American...