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Obama starts out ahead on the Iran deal. It might not last.

The announcement of a long-awaited Iran deal launches the issue back to the American political arena, where a 60-day congressional review period and countless presidential candidates will ensure a lively debate.

So how will the issue play among the American public? Here's a little preview.

Americans support idea of a deal

Public polls show majorities or pluralities of Americans support the broad strokes of the deal, ranging from 46 to 61 percent. The finding of support for a deal is strikingly robust, with supporters outnumbering opponents across a wide range of question wordings and polling firms.

(If you want to see the individual polls: Chicago Council, Fox News, Quinnipiac University, CNN-ORC, USA Today-SuffolkAP-GfKPost-ABC, PPC)

Polls asking single questions on the deal found partisan divisions, with Republicans significantly less supportive. But a detailed February survey by the non-partisan Program on Public Consultation found that after reviewing an extensive issue briefing with arguments for and against a deal, more than 6 in 10 Democrats and Republicans supported making a compromise deal rather than increasing sanctions aimed at forcing the nation to give up its entire nuclear program.

Follow-up surveys in Oklahoma, Virginia and Maryland included details on the initial framework of the deal announced in April and found similar levels of support in the politically disparate states.

Polls in the coming weeks will offer a cleaner test on the actual deal struck by international negotiators -- although polls will not be able to capture all of the many specifics. What's clear is Americans have generally been in a pro-deal mood.

But they don't think the deal will work  

The silver lining for Republicans: However much they support the deal, Americans simply don't trust Iran to abide by a deal restricting its nuclear program -- a fact confirmed by a survey released Tuesday.

The Monmouth University poll found 55 percent saying they don't trust Iran "at all" to dismantle its nuclear program and allow independent inspections (the deal requires Iran to scale back its program, not dismantle it entirely). In a CNN/ORC poll last month, 64 percent expected that negotiations "will not" result in an agreement that prevents Iran from developing nuclear weapons.

The lack of trust in Iran shouldn't be too surprising; more than seven in 10 Americans said Iran was an "enemy" or at least "unfriendly" in a February CBS News poll.

That skepticism stands in stark contrast to the optimism expressed by President Obama announcing the deal Tuesday morning. Obama said,“We have stopped the spread of nuclear weapons in this region.” Americans are clearly more skeptical about the meaning of a deal, and will likely be sympathetic to arguments that the deal does not do enough to stop Iran from producing nuclear weapons.

And Obama's strongly worded comments might not bolster Americans confidence, with his middling job-approval ratings and his deeply partisan image.

[Read: The historic nuclear deal with Iran: How it works]

Where things go from here

The Iran deal marks an immediate foreign policy victory for Obama and could bolster his standing, but the mix of support and skepticism for it makes Americans' reactions to the upcoming debate unpredictable.

Support could sink as the deal immediately faces a wave of scrutiny from several sources: 1. Republican senators and members of Congress building support for a resolution disapproving of the deal; 2. the nearly 20 Republican presidential candidates seeking to break through the crowded field; 3. Israel's leaders and conservative American-Israeli groups; and 4. Some Democrats who are strongly allied with Israel and have expressed skepticism of the deal.

Vocal opposition from these groups didn't do much to temper support for the framework was announced this spring, but the final deal includes many more details to pick apart and a solid 60-day period of congressional review to air concerns. In other words, people will soon learn much more about this, and it will be a much bigger piece of the news.

[Can Congress stop the Iran deal?]

Support for the deal might become more partisan as a result of these debates, with Republicans withdrawing support as big swaths of their party speak out against the agreement. Democrats leaders and voters will be particularly important to watch in the coming weeks. Significant opposition from Democrats would be required for Congress to reach the two-thirds majorities required in both chambers to stop Obama from lifting sanctions against Iran. Tepid support among Democrats could also translate to weak support among Democratic voters at large; Obama has struggled to rally passionate support from his base on foreign policy issues.

In other words, get ready for a very dynamic debate.

Peyton M. Craighill contributed to this report.