WASHINGTON — President Obama all but clinched victory for his Iran nuclear deal on Tuesday, as two Democratic senators threw crucial support behind the landmark accord.

The announcements by the senators, Bob Casey of Pennsylvania and Chris Coons of Delaware, came a week before the Senate was to formally debate a Republican resolution disapproving the agreement between Iran and six world powers.

Mr. Obama would veto any such resolution, and with further announcements of support for the accord expected as soon as Wednesday, any move to override him would almost certainly fail.

Mr. Coons’s decision in particular is likely to have resonance with the few remaining undecided Democrats. As an outspoken member of the Senate Foreign Relations Committee, he expressed grave concerns about the deal before deciding any alternative would be far worse.