As the Republican presidential campaign turns to Super Tuesday this week, one contest looms more super than the rest: Ohio, a state with many of the same economic and electoral dynamics as Michigan but with much more at stake for Republicans.

Whereas Michigan is usually a hope-to state for Republicans in the general election, Ohio is a must-do. No Republican has ever won the presidency without winning Ohio. Thus, the challenge for the GOP candidates is to win the primary next week without turning off voters who they’ll need to carry the state in the fall.

After a bruising couple of weeks in Michigan, where the fight between Mitt Romney and Rick Santorum focused heavily on the kind of controversial social issues that tend to alienate independent voters, Republican officials are worried about the tenor and message of their campaign.

“We need to move on to having a nominee, so we can speak with one voice out there and begin drawing that contrast with Obama,” said Ed Goeas, a Republican pollster who most recently worked for Rep. Michele Bachmann (Minn.), a former presidential contender.

Instead, what is likely to happen is a week of unrelenting attacks from the candidates and their supporters akin to the one that just played out in Michigan — and Florida, South Carolina and elsewhere before that. If anything, the negativity is likely to increase with the full engagement of former House speaker Newt Gingrich, who was a minimal presence in Michigan.

Independent groups backing Romney, Santorum and Gingrich are already airing TV ads in the state. Santorum campaigned in Ohio Tuesday and Romney will be in Toledo Wednesday morning for an event, followed by another in Columbus.

Romney will confront many of the same challenges in Ohio that he faced in Michigan, without the benefit of his hometown connection.

Like Michigan, Ohio’s economy relies heavily on the auto industry, and Romney’s high-profile opposition of the government bailout of the industry is not likely to be received warmly by many voters. He supported an effort last year by Ohio Gov. John Kasich (R) to restrict public unions’ collective-bargaining rights — an effort that was overwhelmingly overturned in the fall by voters in this union-heavy state. And Romney’s courtship of religious voters by supporting, for instance, an antiabortion “personhood initiative,” risks alienating female voters.

“The number one thing is the auto bailout,” said Eric Kearney, a Democrat from Cincinnati and minority leader in the Ohio Senate. “Ohio is the second-largest auto producer in this country. We rely on that. It’s a substantial portion of our economy. The first thing Mitt Romney says, and he repeats it, is he is against the auto bailout. Those are Ohio jobs he’s talking about that he doesn’t want to retain. I don’t get what his strategy is.”

Perhaps more than anything else, however, Romney’s difficulty connecting with average Americans may hurt him in a state such as Ohio. Romney acknowledged on Tuesday that his gaffes — including mentioning his wife’s “couple of Cadillacs” — have not been helpful to his cause. Republicans in Ohio agreed.

“People are like, ‘Yeah, he’s probably going to win, but I really don’t like him, and I’m not going to vote for him,’ ” said a high-ranking Ohio Republican who requested anonymity to speak freely. “That’s the collective zeitgeist.”

Santorum, too, has built a body of statements and positions that threaten his appeal with moderates and independents. His personal opposition to contraception and recent statements criticizing President John F. Kennedy’s defense of church-state separation go against the views of a majority of voters in virtually all public polling.

The two leading candidates are approaching Ohio in markedly different ways. Although Santorum on Tuesday backed away from his criticism of Kennedy, he is not shying away from his embrace of culturally conservative stands, including opposing abortion and criticizing the government for curtailing religious freedom. His goal is to present a clear contrast with President Obama and convince voters that this makes him more, not less, electable in the fall.

Romney, in contrast, is trying to refocus his campaign on the economy, relying heavily on the methods that have served him well in past wins: a well-organized and well-financed ground operation, a heavy emphasis on early-voting recruitment, a growing list of endorsements, including from both establishment and tea-party leaders, and millions of dollars in TV advertisements.

“We always planned for a potentially long and drawn-out nominating process,” Romney spokesman Ryan Williams said.

Even in the states where that strategy has worked, however, it has come at a cost. In Florida, for instance, Romney spent millions attacking Gingrich. He won the primary on Jan. 31, but his own popularity declined at the same time.

The risk of a similar outcome looms large in Ohio. And with each passing contest like it, he has less time to position himself for the general-election contest he hopes to wage against Obama.