Story highlights

President Obama will take questions at a news conference Wednesday

Republicans are finding fault with the complex agreement

A protracted battle is expected, with Congress having 60 days to review the deal

CNN  — 

The talks in recent weeks to reach a comprehensive deal had stretched way past their original deadline of June 30. As recently as late Monday, sticking points remained, including Iran’s insistence on the lifting of an embargo on the sale of conventional weapons and missiles, multiple sources said.

President Barack Obama is due to hold a news conference Wednesday as his administration maneuvers to protect the landmark deal over Iran’s nuclear program that was announced a day earlier.

Critics and supporters are already firing out their arguments over the complex agreement brokered in Vienna, which Congress will have 60 days to review.

Obama began making his case Tuesday, delivering a televised statement and later telling The New York Times that the deal is “the most definitive path by which Iran will not get a nuclear weapon.”

On Wednesday, he will continue the campaign, taking questions from reporters.

His opponents in the political battle over the deal include Republicans in Washington and Israeli Prime Minister Benjamin Netanyahu, who described the deal as “a stunning, historic mistake.”

Squaring up for the fight

Republicans in Congress have vowed to heavily scrutinize the terms of the agreement, with many of them already finding fault with it.

“It’s going to hand a dangerous regime billions of dollars in sanctions relief while paving the way for a nuclear Iran,” said House Speaker John Boehner.

He said Tuesday that if “it’s as bad a deal as I think it is at this moment, we’ll do everything we can to stop it.”

The Obama administration has moved quickly to sell the Vienna plan to Democrats, some of whose votes would be needed by Republicans to pass a resolution of disapproval to block its implementation. Many Democrats are concerned that the accord could leave Israel vulnerable without doing enough to rein in Iran.

Obama warned lawmakers Tuesday that he would veto any measure that would prevent the agreement from going into effect. Overriding the veto in Congress would require a two-thirds majority, a tough challenge for Republican leaders.

All sides are squaring up for a protracted, bruising confrontation.

“The fight over the Iran deal is going to make the Obamacare battles look like two preppies slap-fighting over a cucumber sandwich,” Jeffrey Lewis, an arms control expert, wrote in an article for Foreign Policy.

‘A path for Iran to engage constructively’

Under the agreement reached in Vienna, sanctions that have choked the Iranian economy will be rolled back in return for restrictions on its nuclear activities, which will be inspected by the International Atomic Energy Agency.

Concerns about the terms of the deal include the 24-day notice that inspectors will have to give to visit suspicious Iranian sites.

But many analysts have voiced support for the plan.

“This deal keeps Iran’s nuclear program confined, monitored from every angle, with narrow maneuvering room,” Jacqueline Shire, a former member of the U.N. Panel of Experts on Iran, wrote in an opinion piece for CNN. “It also provides a path for Iran to engage constructively with the world, more necessary now than ever before.”

The agreement is also providing grist for candidates running for the U.S. presidency in 2016, with Republicans lining up to bash it and Democrats offering praise.

Celebrations in Tehran

There was little sign of discord in Iran on Tuesday.

Celebrations broke out on the streets of Tehran after the deal was announced. People cheered and danced. Congratulatory messages poured in on social media, praising President Hassan Rouhani for bringing an end to years of crushing sanctions.

“Negotiators have reached a good agreement, and I announce to our people that our prayers have come true,” Rouhani said in a live address to the nation.

His government will now need to deflect any opposition to the deal from anti-American hardliners in the regime.

Rouhani’s challenge is to navigate between “a hardline minority, which has a monopoly on coercion, and the vast majority of Iranians, who want to see a country which puts its national interest before revolutionary ideology,” said Karim Sadjadpour, a senior associate at the Carnegie Endowment for International Peace.

Key to that effort will be the support of Iran’s supreme leader, Ayatollah Ali Khamenei.

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CNN’s Michelle Kosinski, Elise Labott and Kevin Liptak contributed to this report.