Senator Ron Wyden (D-Ore.), center, speaks with reporters as he departs the Senate floor on Tuesday. He announced his support for the Iran deal. (Jonathan Ernst/Reuters)

A band of undecided Senate Democrats broke in favor of the international nuclear deal with Iran on Tuesday, putting President Obama on the brink of one of the most significant victories of his presidency.

Forty-two senators are now publicly supportive of the Iran deal, all of them Democrats or independents who caucus with Democrats. That would be enough to bottle up Republican attempts to overturn the deal, sparing Obama the drama and embarrassment of having to veto legislation rejecting it.

But the milestone earned a restrained reaction from the White House and other supporters Tuesday. The muted response reflected uncertainty over whether the filibuster margins in the Senate will hold in the face of Republican attacks, a lack of enthusiasm among many Democratic endorsers and a GOP united against the deal.

Announcements in support of the deal Tuesday came from Sens. Richard Blumenthal (D-Conn.), Maria Cantwell (D-Wash.), Gary Peters (D-Mich.) and Ron Wyden (D-Ore.), establishing a margin that would deprive Republicans of the 60 votes necessary to close debate on disapproval legislation and advance it to Obama’s desk.

Also Tuesday, the last undecided Senate Republican, Susan Collins of Maine, announced her opposition, dashing any White House hopes for bipartisan support. A fifth Democrat making an announcement Tuesday, Sen. Joe Manchin III (D-W.Va.), also said he would vote to disapprove of the deal.

The spate of announcements came on the day lawmakers reassembled in Washington after a month-long break, with the Iran deal at the top of a high-stakes list of September business.

With 38 senators — enough to sustain a presidential veto — already publicly favoring the deal coming out of the holiday weekend, the decisions of the remaining undecided had little bearing on the ultimate implementation of the deal.

But the question of whether Democrats would cobble together enough support to prevent the GOP resolution from reaching Obama’s desk has been closely watched on Capitol Hill. Deal backers have worked to maintain steady momentum in support of the pact, and forcing a veto would extend the congressional debate just as many Democrats are hoping to pivot public attention to the next crucial issue: funding the federal government.

Sen. Chris Murphy (D-Conn.) said forcing a veto would amount to a “procedural charade” that would damage Congress’s credibility. “The president’s hand is strengthened in the region and around the world if we don’t have to drag this out for another few weeks,” he said.

At the White House, press secretary Josh Earnest said the administration felt “gratified” by the growing support for the Iran nuclear deal, and he suggested that the White House expects Democratic supporters to filibuster the vote to disapprove the accord.

Supporters “should take the necessary steps in Congress to prevent Congress from undermining the agreement,” Earnest said. He noted that Republicans often used similar methods to “stymie the president’s agenda” when the GOP was in the minority in the Senate.

The prospect of a filibuster prompted sparring between the party floor leaders Tuesday afternoon, moments after the Senate gaveled back to business.

Majority Leader Mitch McConnell (R-Ky.) took aim at Democrats, saying senators “should not hide behind procedural obfuscation to shield the president or our individual views,” arguing that the Iran disapproval should be decided on a majority vote for final passage, not on a procedural vote requiring 60 senators.

But Minority Leader Harry M. Reid (D-Nev.) cited multiple occasions where McConnell threw up procedural roadblocks when Republicans were in the minority. “After the numerous speeches that he has given about the 60-vote threshold on everything important, is he suggesting this Iran agreement is not important?” Reid asked.

Obama aides said the Iran deal has been the White House’s top priority for months, with the president and other top administration officials engaged in a determined lobbying effort with Congress members and interest groups, as well as the general public.

Obama has spoken or met with more than 120 members of Congress since the deal was announced, aides said, and Cabinet officials have briefed more than 220 lawmakers. They emphasized that Obama has continued to talk with lawmakers by phone over the congressional recess, noting that he made 30 calls during his vacation on Martha’s Vineyard in August.

“We feel gratified today,” Earnest said, “because the vast majority of those who did take time to consider the terms of the agreement and to participate in briefings and meetings, and in many cases even hear firsthand from the president . . . indicated their plan to support the agreement.”

Blumenthal, Peters and Wyden had long been considered possible opponents of the deal, given the opposition of the Israeli government and significant elements of the American Jewish community. Blumenthal and Wyden are Jewish, and Peters has close ties to Michigan’s Jewish leadership; all have made comments critical of the deal since its announcement in July.

But all three said in separate statements Tuesday that the deal negotiated by Obama in conjunction with international allies is, while imperfect, the best path forward.

“While this is not the agreement I would have accepted at the negotiating table, it is better than no deal at all,” Blumenthal said.

Wyden said: “This agreement with the duplicitous and untrustworthy Iranian regime falls short of what I had envisioned, however I have decided the alternatives are even more dangerous.”

Said Peters: “Despite my serious concerns with this agreement, I have unfortunately become convinced that we are faced with no viable alternative.”

Manchin was the fourth Senate Democrat to oppose the deal, following Charles E. Schumer (N.Y.), Robert Menendez (N.J.) and Benjamin L. Cardin (Md.).

Manchin, who said in July he was “leaning strongly” toward supporting it, said in a statement that he “could not ignore the fact that Iran, the country that will benefit most from sanctions being lifted, refuses to change its 36-year history of sponsoring terrorism. . . . I cannot gamble our security, and that of our allies, on the hope that Iran will conduct themselves differently than it has for the last 36 years.”

He added that if Iran is caught violating the nuclear agreement, “I have grave doubts that we will have unified, committed partners willing to prevent Iran from obtaining a nuclear weapon.”

Some uncertainty persisted after Tuesday’s announcements, in part because at least one supporter of the deal, Sen. Christopher A. Coons (D-Del.), suggested last week he might not join a filibuster. A spokesman said Tuesday that Coons “simply hopes that the process will happen in a way that makes clear where each senator stands on this critical agreement.”

Sen. Lindsay O. Graham (R-S.C.) suggested a filibuster would be a “blot” on the Senate: “Have we sunk that low? If you really believe this is a good deal, take the floor and tell me why. . . . We all should be on record voting either for it or against it.”

But the debate would be limited in any case: Congress faces a tight timeline for taking action under review legislation passed this year. Lawmakers have until Sept. 17 to weigh in for or against the agreement, and McConnell on Tuesday made procedural moves to limit floor amendments in order to speed consideration the bill.

McConnell said last month that he expects to have a debate beforehand “with the dignity and respect that it deserves” — including the rare spectacle of having all 100 senators at their desks on the floor. On Tuesday, he asked all senators to be present in the Senate chamber starting Wednesday afternoon.

Karoun Demirjian and David Nakamura contributed to this report.