WASHINGTON — Senator Barbara Mikulski of Maryland on Wednesday came out in support of President Obama’s Iran nuclear accord, the 34th Democrat in favor. Her decision gives Mr. Obama the votes needed to assure the deal will survive a congressional challenge.

“Some have suggested we reject this deal and impose unilateral sanctions to force Iran back to the table. But maintaining or stepping up sanctions will only work if the sanction coalition holds together,” Ms. Mikulski, the longest serving female senator in history, said in a statement.

“It’s unclear if the European Union, Russia, China, India and others would continue sanctions if Congress rejects this deal. At best, sanctions would be porous, or limited to unilateral sanctions by the U.S.”

Ms. Mikulski’s decision came a day after Senators Chris Coons of Delaware and Bob Casey of Pennsylvania also announced they would support the deal. With 34 senators favoring the accord between Iran and six world powers limiting the country’s nuclear program, opponents may still be able to pass a resolution disapproving the deal later this month, but they do not have the votes to override Mr. Obama’s promised veto.

And with momentum on their side, the White House and Senate Democrats next week hope to find seven more votes to filibuster the Republican resolution of disapproval. That would ensure the resolution would never leave the Senate, and Mr. Obama would not be forced to use a veto.

Despite the continuing rancor on Capitol Hill, there was also growing recognition, even among some accord opponents, that the other nations — Britain, China, France, Germany and Russia, and especially Iran — would be unwilling to renegotiate the agreement even if Congress formally rejected it.

In most cases, support for the deal has not been enthusiastic, as lawmakers have confronted one of the most divisive policy debates of modern times, with the security of Israel and the stability of the Middle East potentially at stake. But enough Democrats have come to the conclusion that killing the accord would be far worse than approving it.

International sanctions that crippled Iran’s economy and helped bring Tehran to the negotiating table are unlikely to be reassembled now that the United States’ partners have agreed to begin lifting them. And most Democrats have concluded that if Congress rejected the deal, Iran would be able to move more quickly toward a nuclear weapon.

Republicans — backed by Prime Minister Benjamin Netanyahu of Israel — remain implacably opposed to the deal and have vowed to press forward next week with a resolution of disapproval. Senator Bob Corker, Republican of Tennessee and chairman of the Foreign Relations Committee, is asking Democrats not to filibuster the resolution so that it can come to a final up-or-down vote.

How senators respond to that entreaty is still unclear, even if a veto override appears impossible.

Supporters of the deal claimed victory. “After a great national debate that has taken place over the past two months, rational argument, solid analysis and sober reflection have won over wild exaggeration, scaremongering and a flood of money,” said Jeremy Ben-Ami, president of J Street, a Jewish pro-Israel group that supports the nuclear deal.

“Supporters of the agreement, including J Street, were vastly outspent by opponents — but almost every lawmaker who began this debate undecided and was willing to listen to both sides ended up supporting the deal.”