After years of negotiating, the U.S., the European Union and five of the world’s most powerful nations have finally agreed to a nuclear accord with Iran. The media site Al-Monitor called it “a new chapter with Iran.”

Among many professionals, the deal has sold itself. This is the same deal that was announced months ago as a framework, and exceeded all expectations. If anything, it’s better. Ernest Moniz, the nuclear physicist who advised the Obama administration, tweeted, “The #IranDeal is based on hard science. Our nuclear experts & #NationalLabs helped shape the negotiations w/ rigorous technical analysis.”

Former Swedish Prime Minister Carl Bildt said, “Several missed opportunities for Iran deal in past years. Mistrust towards Iran was too dominant. But better late than never?”

“Better late than never” is a wise assessment. Polling has consistently shown the American people support an agreement with Iran. When Ronald Reagan made a deal with the Soviets, Americans were willing to accept his approach of “trust, but verify.”

Today, Americans are in agreement with a more cautious Obama. They accept his word that “this deal is not built on trust. It is built on verification.” Foreign Policy, a publication with but occasional good words for Obama, ran an analysis with the headline: “It’s a Damn Good Deal.”

The author, Jeffrey Lewis, director of the East Asia Nonproliferation Program, was woken at 3 a.m. by a beeping cellphone with the text of the treaty. “Bleary eyed and coffee deprived,” he read the whole text “and I liked what I found.”

When it comes to the politicians in both Iran and the United States, however, acceptance is harder. Congressional Democrats were supportive of Obama, yet, as they are charged with reviewing the agreement, most deferred judgment until they had read the text.

Reporters found Republicans ready with their press releases before the agreement was even announced. Israeli Prime Minister Benjamin Netanyahu, knowing this is a history-making deal, attempted to piggyback on the headlines by saying it was a “mistake of historic proportions.”

Iran’s minister of foreign affairs and chief negotiator at Vienna, Javad Zarif, had it no easier. The New Yorker reported that, “Some (Iranian) lawmakers suggested impeaching Zarif. One hardliner called him a ‘traitor.’” The magazine concluded, “For both sides in Vienna, the adversaries back home may prove more formidable than those across the table.”

The Republican leadership has had a media blitz prepared for weeks. When lawmakers go home in August, special interest lobbyists affiliated with them will throw millions of dollars into districts to intimidate Democratic congressmen.

Congress has a say. It should have a robust debate. But the president has a veto that he will use. It will take two-thirds of each chamber to override Obama’s veto. That’s 290 votes in the House, and 67 in the Senate — an unlikely scenario without large-scale defections of Democrats.

Let’s not forget that Obama ran on this, and won twice, both with strong progressive backing and a strong majority of the country choosing diplomacy over war. This is what diplomacy looks like: hard-nosed negotiations, which don’t yield either side’s ideal outcome, but through which we can get the core things we want. In this case, an Iran with no path to a nuclear weapon.

We don’t have to imagine the alternative, because we saw it for nine years in Iraq, which is why we chose Obama’s path in the first place. This is something every Democrat should be proud of, and every American should embrace as a fresh start.

This is a victory for the whole world — a deal negotiated by all of the world’s major powers. It’s telling that Netanyahu directed his full ire at Obama, but had not a single cross word for the leaders of Britain, China, France, Germany, Russia and the European Union. They were all present at the table. All have deeply vested interests in the outcome, and all had their input.

Let’s be real here: What made this deal so tricky was creating a situation that genuinely blocked every path to a bomb while allowing Iran dignity. The deal allows its leaders to avoid looking as if they’d inflicted years of suffering and sanctions on their people for nothing.

We now have extremely effective means of accountability up and down Iran’s supply chain to make certain they are not working on a weapon. If they break the deal or cheat, we will catch them, and sanctions will go back on.

This deal is a compromise. That means nobody got everything they wanted and all had to give up things they really wanted. It does not end Iran’s peaceful nuclear program. It does freeze any attempt at nuclear weapons for periods from 10 to 25 years, giving us time to make the deal permanent.

Establishing contact with Iran allows us to influence Iran in ways that would otherwise be limited to military action. Iran is still outrageously sponsoring arms to Hamas and Hezbollah. It has formed a cyber-warrior team that has the same elite status as its nuclear scientists. But neither Russia nor China were model nations when Reagan made a nuclear arms deal and Nixon recognized China. Those acts of diplomacy did not end the ideological conflicts, but they did make the world safer.

This deal is the same leap of faith that Nixon and Reagan took. In their cases, it paid off. President Obama, like his predecessors, is not naive. He knows who he’s dealing with. But, as Benjamin Rhodes, a key national security adviser to Obama, said, “The president said many times he’s willing to step out of the rut of history (to stop) a spiral towards conflict.”

Donna Brazile is a senior Democratic strategist, a political commentator and contributor to CNN and ABC News, and a contributing columnist to Ms. Magazine and O, the Oprah Magazine.