(Adds comment from Feinstein, Hoyer, Corker interview, Biden meeting with House Democrats, timing of House and Senate votes)
By Patricia Zengerle
WASHINGTON, July 14 (Reuters) - The nuclear deal between world powers and Iran starts a new phase of intense negotiation - this time between the Obama administration and the U.S. Congress, where some Republicans have long been working to sink an agreement.
Any effort in Congress to overturn the deal will face an uphill fight. Republicans have majorities in both the House of Representatives and Senate, but they would need the support of dozens of President Barack Obama's fellow Democrats to sustain a "resolution of disapproval" that could cripple a deal.
The odds of that are slim. A resolution of disapproval would need only the Republican majority to pass the House, but would require at least six Democrats to get the 60 votes needed to advance in the Senate. The chances of mustering enough support to then overrule an Obama veto are slimmer still.
Obama vowed on Tuesday that he would veto any bill Congress passed that would prevent implementation of the Iran agreement.
Nancy Pelosi, who leads the Democrats in the House, praised Obama in a statement. "I commend the president for his strength throughout the historic negotiations that have led to this point," she said, promising Congress would "closely review" the agreement.
Senate Democrats have stood firm so far against Republican-led efforts to interfere with the talks between Iran, the United States and five other world powers. Some expressed skepticism about the deal, but others said they expected to vote for it.
Senator Dianne Feinstein, a veteran Democrat who is the ranking member of the Senate Intelligence Committee, said she would support the deal. "This is a strong agreement that meets our national security needs and I believe will stand the test of time," she said in a statement.
In the House, more than 150 Democrats, including Pelosi, signed a letter in May that strongly supported the negotiations.
"I understand the heavy lift that's involved," Tennessee Republican Senator Bob Corker, chairman of the Senate Foreign Relations Committee, told reporters when asked about the chances of passing a "resolution of disapproval".
Corker said the Foreign Relations committee would review the deal closely but added he would begin "from a place of deep skepticism" about whether the agreement meets the goal of preventing Iran from obtaining a nuclear weapon.
Other leading Republicans went much further in their criticism. House Speaker John Boehner promised a fight.
"Instead of stopping the spread of nuclear weapons in the Middle East, this deal is likely to fuel a nuclear arms race around the world," Boehner said in a statement.
Obama in May signed a law, authored by Corker, giving Congress the right to review the agreement and potentially sink it by passing a disapproval resolution that would eliminate the president's ability to waive sanctions passed by Congress.
Easing sanctions is an integral part of the deal, under which Iran will curtail its nuclear program.
Under the Iran Review Act, lawmakers have 60 days to review the agreement and decide how to respond, once they receive the agreement and supporting documentation. During that period, plus 22 more days in which Obama could veto a resolution and Congress could try to override it, Obama cannot waive the congressional sanctions.
A veto override would require a two-thirds majority in both houses, or 13 Democrats along with all 54 Republicans in the Senate, and 43 Democrats plus all 236 House Republicans.
Sanctions passed by Congress account for the overwhelming majority of those imposed by the United States. U.S. sanctions are central to the international regime because of the country's influence on global trade and banking.
Congressional briefings on the Iran deal have already begun. Vice President Joe Biden was to meet with House Democrats on Wednesday morning to discuss Iran, and Obama and other administration officials called several lawmakers on Tuesday.
Acknowledging the difficulty of passing a disapproval resolution, some lawmakers suggested Congress should consider, and then reject, a "resolution of approval."
Defeating such a resolution by a large margin would not affect the sanctions regime, but it would send a strong message that the United States is not united behind a "bad" pact and was prepared to act if Iran moved toward building a bomb, they said.
Corker told Reuters in an interview that congressional leaders would decide whether to pursue a resolution of approval or disapproval in the coming weeks. But neither the full House nor Senate is expected to vote on any measure before September, after lawmakers' August recess.
Steny Hoyer, the number-two Democrat in the House, dismissed concerns that the delay would leave Democrats vulnerable to a summer of attacks from Republicans that they will be voting "for Iran" if they back Obama.
"I'm not sure that it's politically disadvantageous to members," he told reporters. "I think the American public may well agree with the president on this."
Both parties acknowledged that the debate will not end this year. Some lawmakers have discussed imposing more sanctions over Iran's human rights record or for supporting terrorism.
The Iran Review Act requires the president to regularly certify that Tehran is adhering to terms of a deal. There is no guarantee the next president would do so. Most Republican 2016 White House hopefuls said they do not support the deal. (Additional reporting by Idrees Ali, Roberta Rampton and David Lawder; Editing by David Storey, Stuart Grudgings, Jeffrey Benkoe and Ken Wills)