The White House has said it is “confident” of reaching a final deal over Iran’s nuclear programme by an end-of-June deadline.
A framework agreement struck on Friday will see Iran curb nuclear activities in return for relief from sanctions.
US Republicans sceptical to the deal have threatened to derail it or impose new sanctions.
President Obama said he had begun efforts to win over sceptical members of Congress.
Mr Obama spoke to all four congressional leaders on Friday, White House spokesman Eric Schultz said.
Republicans control both US Houses of Congress, and there is bipartisan support for a bill which would give Congress the right to review any deal before sanctions are lifted. Mr Obama has threatened to veto it.
In his speech on Thursday hailing the deal, the president anticipated his critics.
“If Congress kills this deal not based on expert analysis, and without offering any reasonable alternative, then it’s the United States that will be blamed for the failure of diplomacy.”
Despite the domestic pressure, the White House gave another upbeat assessment of the deal.
“We defied the odds,” Mr Schultz said. “I do think there’s a lot of work to be done, but we are confident that we can get those details in place.”
Iran’s President, Hassan Rouhani, has vowed it will abide by the terms of the preliminary nuclear agreement it signed with six world powers, so long as they do too.
He said the deal marked a step towards changing Iran’s relationship with the world: “Today is a day that will remain in the historic memory of the Iranian nation.
“Some think that we must either fight the world or surrender to world powers. We say it is neither of those, there is a third way. We can have co-operation with the world.”
Mr Rouhani is also expected to face opposition from conservative critics at home, although clerics praised the agreement at Friday prayers.
Israeli Prime Minister Benjamin Netanyahu warned that it posed a grave danger to the region, in particular his own country.
He said any comprehensive accord, due before 30 June, had to include a “clear and unambiguous Iranian recognition of Israel’s right to exist”.
Under Thursday’s terms, Iran must slash its stockpile of enriched uranium that could be used in a nuclear weapon and cut by more than two-thirds the number of centrifuges that could be used to make more.
In return, UN sanctions and separate measures imposed unilaterally by the US and EU will be gradually suspended as the global nuclear watchdog, the International Atomic Energy Agency (IAEA), confirms Iranian compliance.