WASHINGTON — Fresh from his slim victory in Tuesday’s Ohio presidential primary, former Gov. Mitt Romney is now running against the modern history of the Republican Party as much as his three GOP challengers.

Romney won six of Tuesday’s 10 contests and hauled in 220 delegates, giving him a wide lead in the delegate count.

But unless he quickly seizes control of the race, some Republicans fear the party could face its first contested convention since 1976 when a divisive struggle between President Gerald R. Ford and Ronald Reagan led to Ford’s defeat in the fall to Democrat Jimmy Carter.

Romney, with wins in Ohio, Michigan and Florida, has amassed 415 delegates to the Tampa convention.

That is compared to 176 for former Pennsylvania Sen. Rick Santorum, 105 for former House Speaker Newt Gingrich, and 47 for Texas congressman Ron Paul.

While Santorum and Gingrich have little chance to win enough delegates for a first-ballot nomination, they could make it impossible for Romney to reach the magic number of 1,144, which would offer Americans a throwback to a long-gone era when nominees were chosen in closed-door meetings at the conventions.

And should Romney fail to secure a victory on the first few ballots, the Republican delegates could select a different nominee, such as former Florida Gov. Jeb Bush. Not since Democrats tapped Vice President Hubert Humphrey in 1968, has a nominee not competed in a single primary.

“As long as you have three candidates in the mix winning states, it’s really hard — if not impossible — for someone to get a majority,’’ said Barry Bennett, a Republican consultant in Washington and producer of a film critical of Romney’s business practices.

“And what happens next?’’ Bennett said. “I think that we are at least headed to a contested convention. Nobody wins on the first ballot. Second or third ballot, they can bring in a new candidate. At that point, they would throw a ticker-tape parade for Jeb Bush.’’

To win a first-ballot nomination, Romney needs to win roughly 740 of the remaining 1,416 delegates. And in some of the states where he must collect those delegates — Alabama, Pennsylvania, Mississippi — he is not expected to perform well.

Jack Pitney, a professor of political science at Claremont McKenna College, said he thinks Romney will have a majority before the convention. “But it might take awhile,” he said. “At some point, Republican contributors and activists will recognize that he’s going to be nominated, and Santorum and Gingrich will find it harder to get support. I don’t think we’ve reached that tipping point yet.”

The Republican establishment would clearly like to bring the divisive primary campaign to a close. Just last week, House Majority Leader Eric Cantor of Virginia became the latest senior Republican to endorse Romney.

Ron Bonjean, a one-time adviser to former House Speaker Dennis Hastert, R-Ill., said “most Republicans would like to avoid” any kind of contested convention, adding that “they would like a consensus front-runner who everyone can rally around … rather than deal with Republican infighting about who the best nominee would be.’’

Romney attempted to downplay any possibility of a contested convention. In an interview on CNBC, he said, “We’ve got the time and resources and a plan to get all the delegates. We think that will get done before the convention. But one thing I can tell you for sure is there’s not going to be a brokered convention where some new person comes in and becomes the nominee,” he said. “It’s going to be one of the four people that are still running.”

Throughout much of American history, the contested convention was the norm. Democrats conducted 103 ballots in 1924 before settling on former U.S. Solicitor General John W. Davis as their nominee, while Republicans in 1948 took three ballots to nominate former New York Gov. Thomas E. Dewey over Ohio Sen. Robert A. Taft.

Senior officials in both parties saw their power diluted in the early 1970s when Democrats and Republicans decided to have delegates largely chosen through contested primaries. Except for the 1976 convention fight, every nominee during the past four decades has been known before the convention.

Analysts say that the major obstacle between Romney and the nomination is Romney himself. While he has raised millions of dollars and surrounded himself with a savvy team of advisers, he has failed to offer a compelling political message that can win the votes of the party’s most conservative voters.

Tuesday’s Ohio vote totals tell the tale: Romney won 19 counties, all of them in the metropolitan areas around Cincinnati, Dayton, Columbus and Cleveland-Akron. The remaining 69 counties — including many of the most conservative counties in Ohio — all went to Santorum.

Romney’s barrage of harsh commercials may also have alienated some Republicans. “They drop bombs from the sky … against all their opponents,” said Mary Anne Marsh, a Boston Democratic consultant, about Romney’s strategy.

Still, Romney remains within striking distance of President Barack Obama, trailing 50-44, according to a Wall Street Journal/NBC News poll last week. But if that changes and the race looks to be getting out of reach, Bennett said conventional delegates won’t stay loyal to Romney.

“I know these delegates,’’ he said. “None of them took a blood oath to support who they are supporting. If we get to the convention and Mitt Romney can’t get to 1,144 and there is a poll that says Bush beats Obama and everyone else loses, I think we will be electing someone else.”