In a sign of how difficult the coming talks will be, some differences emerged between U.S. Secretary of State John Kerry and his Iranian counterpart in their public presentation of a key part of the deal - whether or not Iran preserved the right to enrich uranium.
Obama also has to persuade its ally Israel, whose Prime Minister Benjamin Netanyahu denounced the deal as a "historic mistake," that the accord will reduce and not increase the threat from its arch foe Iran. And he has to sell the accord to skeptics in Congress, including some in his own Democratic Party, who have been pressing for more sanctions on Iran.
The breakthrough accord was reached in the middle of the night at talks in Geneva between Iran, the United States, China, Russia, France, Britain and Germany. It won the critical endorsement of Iranian clerical Supreme Leader Ayatollah Ali Khameini and marked a clear turn in a U.S. relationship with Iran that has been fraught since the 1979 Islamic Revolution, and vexed for years over the Iranian nuclear program.
But nobody doubted that tough work lies ahead in moving on from the initial deal that allows a six-month period of limits to Iran's nuclear program in exchange for up to $7 billion worth of sanctions relief, while leaving both the program and the sanctions in place.
"Now the really hard part begins and that is the effort to get the comprehensive agreement, which will require enormous steps in terms of verification, transparency and accountability," Kerry said as he began a meeting with British Foreign Minister William Hague in London.
The agreement, which halts Iran's most sensitive nuclear activity, its higher-grade enrichment of uranium, was tailored as a package of confidence-building steps towards reducing decades of tension and ultimately creating a more stable, secure Middle East.
Iranian Foreign Minister and chief negotiator Mohammad Javad Zarif flew home from Geneva to a welcoming crowd, a reflection of the relief felt by many Iranians exhausted by isolation and sanctions that have been particularly punishing in the last two years.
Zarif said in an interview broadcast on state television that Iran would move quickly to start implementing the agreement and it was ready to begin talks on a final accord.
"In the coming weeks - by the end of the Christian year - we will begin the programme for the first phase. At the same time, we are prepared to begin negotiations for a final resolution as of tomorrow," Zarif said.
Illustrating the delicate dance that looms, he and Kerry differed in their public descriptions of the part of the agreement regarding Iran's right to enrich uranium.
Sunday's agreement said Iran and the major powers aimed to reach a final deal that would "involve a mutually defined enrichment programme with mutually agreed parameters consistent with practical needs, with agreed limits on scope and level of enrichment activities."
Before heading to Geneva, Zarif had a crucial meeting with Khamenei in the presence of Rouhani, a senior member of the Iranian delegation said.
"The leader underlined the importance of respecting Iran's right to enrich uranium and that he was backing the delegation as long as they respected this red line," said the delegate.
What emerged in the text on Sunday was wording that both sides could live with.
Speaking on Iran's Press TV, Zarif said the deal was an opportunity for the West to restore trust with Iran, adding Tehran would expand cooperation with the International Atomic Energy Agency, the U.N. nuclear watchdog, to address what he called some concerns.
"In the final step, the (uranium) enrichment process will be accepted and at the same time all the sanctions will be lifted," Zarif said.
However, on the ABC News program "This Week," Kerry stressed that such a right would be limited and would come about as a result of future negotiations.
He said that under the terms of the agreement, "there will be a negotiation over whether or not they could have a very limited, completely verifiable, extraordinarily constrained program, where they might have some medical research or other things they can do, but there is no inherent right to enrich..."
CRITICS AT HOME AND ABROAD
The deal also leaves Washington with the task if patching strained ties with its staunch Middle East ally Israel.
Obama telephoned Netanyahu to reassure him that Washington would continue to stand by Israel and to suggest that the United States and Israel should quickly start consultations on the Iranian nuclear issue.
Obama - who raised the idea of a rapprochement with Iran when he was campaigning ahead of his first presidential election win in 2008 - will also have to deal with critics at home.
On Sunday, even some of his fellow Democrats were strongly critical of the pact. Senator Charles Schumer of New York, the No. 3 Democrat in the Senate and a Banking Committee member said: "A fairer agreement would have coupled a reduction in sanctions with a proportionate reduction in Iranian nuclear capability."
But it seemed likely that Congress will give him room to see if the agreement works.
Democrats such as Senator Robert Menendez of New Jersey, who chairs the Senate Foreign Relations Committee and is known as a hawk on Iran, made clear that any new sanctions would include a six-month window before they took effect. That would allow time to see if Iran is sticking by the pact.
Senators have been discussing for months imposing even tighter Iran sanctions, which could anger Tehran and put Sunday's interim deal reached in Geneva in jeopardy. And pro-Israel lobbying organizations - among the most effective interest groups in Washington - have failed so far to persuade lawmakers to tighten the sanctions screw on Iran.
The agreement does not need to be ratified by Congress and Obama is using his executive power to temporarily suspend some existing U.S. sanctions on Iran.
The deal halts Iran's progress on its nuclear program, including construction of the Arak research reactor. It will neutralize Iran's stockpile of uranium refined to a fissile concentration of 20 percent, which is close to the level needed for weapons, allow increased U.N. nuclear inspections, and halt uranium enrichment over a fissile purity of 5 percent.
In return the accord grants about $7 billion in potential relief from sanctions. It will allow a potential access to $1.5 billion in trade in gold and precious metals and the suspension of some sanctions on Iran's auto sector and petrochemical exports, and also give Iran access to some $4.2 billion in sales from its reduced oil exports.