US President Barack Obama has won the backing of a fresh clutch of senators for his Iran deal, raising the prospect he could yet dodge a humiliating legislative rebuke.

For months, Republicans and rebellious Democrats have looked on course to pass a resolution against the nuclear deal, a stinging rejection of a central Obama foreign policy goal.

But, with 15 Senate Democrats backing the deal in as many days -- including Senate minority leader Harry Reid and Michigan's Debbie Stabenow on Monday -- the White House may dodge a political bullet.

A 'no' vote next month would not be enough to scupper the whole nuclear agreement -- thanks to Obama's veto power -- but it could foreshadow trouble ahead.

It could empower the next president to upend the deal and signal problems in lifting Congressionally mandated sanctions, a crucial part of the agreement as far as Tehran is concerned.

Congress often tries to influence foreign policy, but the 1999 rejection of the Comprehensive Test Ban Treaty is one of only a handful of recent examples of lawmakers repudiating a president's top foreign policy priority.

Even George W. Bush's contentious war in Iraq won Congressional approval.

- Managing expectations -

The White House, facing a momentous defeat, has tried hard to lower expectations.

In public it has long appeared resigned to losing the initial vote, and to the need for a presidential veto.

"Our goal all along has been to build as much support in Congress as we possibly can," said spokesman Josh Earnest on Monday.

"What we have been focused on is building the kind of support that we need in both the House (of Representatives) and the Senate to sustain a presidential veto."

But with just two Democrats publicly opposed to the deal -- with a half dozen waverers still undeclared -- the vote in the Senate looks like being tight.

Behind the scenes those in favor of the deal are lobbying furiously to avoid the veto, with campaign donors threatening to withhold future funding.

"A majority in the House for the resolution of disapproval is probably certain," said Corey Boles, a senior analyst with the Eurasia Group.

"It is an open question whether opponents of the deal will be able to muster the necessary 60 votes in the Senate to advance the measure."

Republicans need the support of a total of six Senate Democrats to pass a resolution against the deal.

So far they have won over two -- New York's Chuck Schumer and New Jersey's Bob Menendez.

The White House needs 41 votes to forestall the resolution, and just 34 Senate votes to uphold Obama's veto.

So far 28 Democrats have declared their support for the deal.

"Forty-one is definitely possible," said Jamal Abdi of the National Iranian American Council, which has been lobbying fiercely in favor of the agreement.

"A number of important swing votes have broken our way. The opposition still needs to find four more Democrats to cross lines," he said.

"If I were them I would be sweating now."