WASHINGTON (AP) ― The months of turmoil among Republicans bidding to become the party nominee to challenge President Barack Obama head into a final sorting process in Iowa next week with Mitt Romney and Ron Paul leading a field of seven candidates.

Romney, the former Massachusetts governor, and Paul, a long-serving Texas congressman, are running neck-and-neck in the Midwestern state that holds precinct nominating caucus meetings Tuesday night.

The caucuses are a test of the campaign financing and organization that can winnow candidates who fail to finish in the top tier.

Obama’s approval ratings have improved slightly, but he remains vulnerable because of Americans’ dissatisfaction with his handling of the economy and it’s laggardly recovery from the Great Recession.

But the chaotic nature of the Republican race, in which a series of candidates have shot to the top of the field and just as rapidly lost support, has been a gift to Obama, diverting attention from the difficult politics surround his hopes for re-election in November.

Romney lashed out at Paul for the first time Wednesday over his position that the United States should not concern itself over Iran’s suspected nuclear weapons program.

“One of the people running for president thinks it’s okay for Iran to have a nuclear weapon,” Romney said as he campaigned in Muscatine, an eastern Iowa city. “I don’t,” he said in response to a question from someone in the audience.

Texas Gov. Rick Perry was of a similar mind.

“You don’t have to vote for a candidate who will allow Iran to have a nuclear weapon to wipe Israel off the face of the earth. Because America will be next,” Perry said in Urbandale, reiterating a line of argument from a day earlier.

“I’m here to say: You have a choice,” Perry added.

As if in rebuttal, Paul’s campaign launched a new television ad describing him as “principled, incorruptible, guided by faith and principle” and the man to restore the economy. “Politicians who supported bailouts and mandates, serial hypocrites and flip floppers can’t clean up the mess,” it says as photos of former House speaker Newt Gingrich and Romney appear on screen.

Paul has come under attack as his long-shot campaign has surged in Iowa where some polls have him in the lead.

With Gingrich quickly fading from the top tier after being targeted by a barrage of attack ads, Iowa voters are about evenly split between the more moderate Romney and the extreme libertarian views of Paul.

But many Republican conservatives across the country distrust Romney because of his past positions on abortion, gay marriage and health care. Paul, meanwhile, is seen as too extreme by mainstream party voters.

The Iowa caucuses likely will force some candidates to drop out of the race and shape the coming six-month string of state-by-state primary elections and caucuses leading up to the Republican National Convention in August that officially names a candidate.

Romney, who returns to Iowa Wednesday, has projected the confidence of a front-runner as he looked past his Republican rivals and accused Obama of “misguided policies and weak leadership.”

As if previewing the themes of a general election campaign, Romney said Tuesday that in his campaign travels, “I’ve heard stories of The Great Obama Recession, of families getting by on less, of planned-for retirement replaced by jobs at minimum wage,” he said during campaigning in New Hampshire, which holds its primary Jan. 10.

He said of Obama: “Gone is the ‘hope and change’ candidate. ... Instead the campaigner-in-chief divides Americans, engages in class warfare and resorts to distortion and demagoguery.”

Aides added that by design, Romney spoke not far from where Obama campaigned four years ago this week en route to an Iowa caucus victory that set him on the road to the presidency.

Romney, making his second run for the nomination, has relied on a well-funded and disciplined organization, generally strong debate performances and deep-pocketed allies to keep his balance as others have risen to challenge him and fallen back.

Romney’s biggest challenge is the distrust of him among many conservative Republicans who have split their support among several candidates whose policy promises are more palatable to them, including Gingrich, Perry, Minnesota Rep. Michele Bachmann and former Pennsylvania Sen. Rick Santorum.

Also in the contest is former Utah Gov. Jon Huntsman, who decided not to focus on Iowa but, instead, to try to make his stand in New Hampshire.