In this April 2014 file photo, Sen. Tim Kaine (D-Va.) speaks to reporters outside the White House. (AP/Pablo Martinez Monsivais)

Three Senate Democrats announced Tuesday that they will vote to support the Iran nuclear deal when it comes before Congress next month, lending momentum to President Obama's push to convince the undecided -- most of whom are his fellow Democrats.

The decisions of Tim Kaine (Va.), Barbara Boxer (Calif.), and Bill Nelson (Fla.) were not especially surprising on an individual basis, but they represent the sort of rank-and-file Democrats that Obama cannot afford to lose if he wants to sustain the centerpiece of his foreign policy agenda. And, coming together, the decisions show that objections raised by Republicans in recent weeks over inspections, sanctions relief and secret "side agreements" have not been enough to keep Democrats on the fence going into the summer recess.

[Iran nuclear deal’s fate in Congress rests with undecided Democrats]

Kaine, a member of the Senate Foreign Relations Committee, had telegraphed his guarded support during a hearing with top administration officials last month, when he indicated that he had doubts about the merits of any alternatives to the pending deal. In a floor speech Tuesday, Kaine called the deal "far preferable to any other alternative, including war."

"America has honored its best traditions and shown that patient diplomacy can achieve what isolation and hostility cannot," he said.

Sen. Chris Coons (Del.), one of the Democrats who has remained studiously undecided, said Kaine's views in particular would help in his own making his own decision. “I respect Sen. Kaine. He’s a good colleague and a very thoughtful member,” Coons said.

[Virginia Sen. Tim Kaine backs Iran nuclear deal]

The decisions of Boxer and Nelson have been under scrutiny, as well. Boxer is also a Foreign Relations member, one of 10 Jewish senators, and a politician who has enjoyed close ties to members of the pro-Israel community who are now strongly against the deal. In a statement Tuesday, she called the deal "the only viable alternative to war with Iran." Nelson is a centrist on foreign policy and defense issues and, because he represents a state with a large Jewish population, had been targeted by deal opponents.

Nelson said on the Senate floor Tuesday that he will vote in favor of the deal "unless there is an unexpected change in the conditions and facts," citing the need to work in concert with allies and keep Iran's "breakout time" to a minimum.

The three Democrats join five others who have announced explicit support for the deal: Richard J. Durbin (Ill.), Dianne Feinstein (D-Calif.), Martin Heinrich (D-N.M.), Tom Udall (D-N.M.) and Elizabeth Warren (D-Mass.). Many other Democrats have made supportive statements but have stopped shy of declaring their unequivocal backing.

[Our continuously updated whip count of where the Senate stands on the Iran deal]

On Wednesday, Foreign Relations members will hold a fourth public hearing on the deal, this one focused on implications in the Middle East, and will also have a private briefing with Yukiya Amano, director of the International Atomic Energy Agency, which has entered into the controversial "side agreements" with Iran.

While the decisions announced Tuesday are not alone sufficient to guarantee the deal's success, they make it harder for opponents to count to the 67 Senate votes needed to override a presidential veto -- or even the 60 votes necessary to beat a Democratic filibuster.

But Republicans are determined to continue the debate, hoping that opposition might mount over the summer break. On Tuesday, House Foreign Affairs Committee Chairman Ed Royce (R-Calif.) introduced a disapproval resolution that will likely become the legislative vehicle for the congressional Iran vote. "It is clear that this is a bad deal, and the House will vote on disapproval in September," said House Majority Leader Kevin McCarthy (R-Calif.).

In the Senate, Majority Leader Mitch McConnell (R-Ky.) is promising to hold a serious, even solemn debate. On Tuesday, McConnell said he hopes to reserve floor time in September for a spectacle rarely seen in the upper chamber: an old-school, honest-to-goodness debate, where committee business is postponed and all 100 senators are expected to sit at their desks on the Senate floor and hear each other out.

"I think this issue's of such magnitude that it's my hope we will ... actually have a debate that rises to the occasion that this seems to require," he said.

Paul Kane contributed to this report.