Maybe Rand Paul’s not such a longshot after all.

This poll was conducted after the deal was announced so the results are, in theory, a referendum on the specific terms. Emphasis on “in theory”: I doubt one voter in a hundred could summarize the details of the agreement. Any poll like this is necessarily a test of how voters feel about a deal in the abstract, not the one we actually have. Verdict: They … kind of like the idea, sort of.

Thirty-one percent of Republicans favor a new nuclear deal with Iran, creating a challenge for their party’s lawmakers who largely oppose the framework accord sealed between Tehran and world powers, a Reuters/Ipsos poll showed on Wednesday.

Another 30 percent of Republicans oppose the pact, while 40 percent are not sure, according to the poll, which revealed a sharp split in the party as its leaders ramp up opposition to the deal championed by President Barack Obama, a Democrat…

The poll showed little support among members of both parties for using military force as a sole method for preventing Iran from developing a nuclear bomb. Five percent of Democrats supported such an option, along with 11 percent of Republicans and 6 percent of independents.

Support for the combined use of diplomatic channels along with military force was higher, however. Fifty percent of Republicans favored that combination, along with 35 percent of Democrats and 42 percent of independents.

Nothing unusual about the topline number. Every poll I’ve seen recently finds mild support for the deal (or “a” deal) on balance. A Fox News survey taken a week ago has it 47/44 in favor of a deal that would end economic sanctions for 10 years in return for Iran “stopping” its nuclear program over the same period. (The actual deal doesn’t do that, of course. Iran will continue to enrich uranium at Natanz, albeit only at low levels.) A WaPo/ABC poll released the same day found a 59/30 split in favor of a deal that would trade sanctions relief for Iran “restricting” its nuke program. Another poll from Pew released a day earlier discovered a 49/40 split in support of negotiating with Iran, which isn’t the same as approving of the deal reached but may amount to that given public ignorance about the terms.

The amazing thing about those three polls is that, despite being pro-deal, voters consistently say they don’t trust Iran. Fifty-five percent told Fox that the United States shouldn’t trust anything Iran says; 59 percent told WaPo/ABC that they’re not confident a deal would prevent Iranian from building nukes; 63 percent told Pew that Iranian leaders aren’t serious about addressing America’s nuclear concerns. How do you square that with support for negotiations? The answer, I think, is in the last paragraph of the excerpt above. Even among Republicans, even when you offer them the option of diplomacy and military action to stop Iran from getting the bomb, Reuters couldn’t do better than 50 percent support. That’s awfully good news for Obama, whose chief goal at this point in striking a bargain with Iran is to push military action fully off the table. (“The threat of war now constrains the West more than Iran,” as Henry Kissinger and George Shultz put it.) Maybe, like O, the public’s learned to live with the idea of containing rather than preventing a nuclear Iran. That’s how you can be pro-deal even while suspecting that any deal will be ineffective. It avoids war and that’s what’s important, whatever that means for Iran’s nuclear capabilities.

One alternate theory: Maybe these poll results boil down simply to the public wanting to at least give Iran a chance to prove their skepticism wrong. Voters are pro-deal — for now. As soon as there’s hard evidence that Iran’s cheating, though, sentiment could shift sharply. In other words, maybe it’s not that voters have ruled out war as that they’ve ruled out preventative war, which didn’t go so well in Iraq. If that’s true then opinion will turn on Obama once there’s proof that Iran’s making him a sucker of him. Which, if you believe Iran’s state media, is happening already. Exit question: Is this story mere Iranian propaganda, designed to placate the deal’s naysayers at home, or are they already laughing in O’s face?