Long after Barack Obama has left office, the newly minted nuclear agreement with Iran will stand as one of the defining moments of his presidency, along with such successes as the Affordable Care Act and unsolved problems including the rise of terrorist threats after the U.S. withdrawal from Iraq.

The agreement will ultimately be judged by whether it halts Iran’s nuclear ambitions and perhaps improves broader U.S. relations with Tehran. But its immediate success will depend on Obama’s ability to manage the political fallout to ensure American acceptance.

The president got off to a strong start Tuesday morning with a comprehensive 14-minute statement countering major opposition arguments. He said, “This deal meets every single one of the bottom lines that we established,” and he warned that “no deal means no lasting constraints on Iran’s nuclear program.”

But his words won’t forestall a bitter battle in the two months Congress set for review. Republican congressional leaders and presidential hopefuls were almost unanimously critical, as was Israeli Prime Minister Benjamin Netanyahu, their close ally. Democratic leaders backed Obama, but others expressed concerns.

Obama said he would veto any congressional effort to scuttle the agreement, meaning opponents would need two-thirds of both houses to block it. That may be difficult, since it requires a significant number of Democrats.

Over the coming months, three key questions will be crucial:

Can experts make the case that the agreement will achieve its goal of preventing Iranian development of a nuclear weapon for at least a decade?

Critics have long had questions about the degree to which Iranians would have to dismantle their nuclear program, the extent of international inspections to ensure compliance, the timetable for dismantling economic sanctions and the future of the international arms embargo on Iran.

Obama said Iran must reduce its nuclear stockpile “to a fraction of what would be required for a single weapon.” Under the plan, international inspectors will have “24/7 access to Iran’s key nuclear facilities,” sanctions relief will be phased in “as Iran takes steps to implement this deal,” and Iran must show compliance before embargoes are lifted, in five years for conventional arms and eight for missiles, he said.

Former Secretary of State Hillary Clinton said it “will have to be enforced vigorously, relentlessly.”

Is the administration right to claim that this is the best possible deal and that the alternative would give Iran the go-ahead to develop a nuclear weapon?

Critics argued that Obama was too eager to reach an agreement and that stricter economic sanctions would have forced further Iranian concessions. But the Iranians faced domestic political pressures against yielding more, and U.S. allies opposed stiffer sanctions. More likely, failure to agree would remove any barrier to Iranian nuclear weapons development.

Some hard-liners favor a military attack to destroy Iran’s nuclear facilities, but military experts question the efficacy.

Can Obama counter predictable opposition from Israel and its congressional allies by mobilizing enough public support to prevail?

On one thing supporters and opponents agree: Iran remains a major sponsor of international terrorism, guilty of what Clinton understatedly called “bad behavior.”

That may be the biggest barrier toward approval of an agreement Obama sought from the outset of his presidency and is on the verge of achieving.

–Carl P. Leubsdorf is the former Washington bureau chief of the Dallas Morning News.