Brokered conventions happen when no candidate has enough delegates to lock up the nomination by the time the party's convention rolls around in late summer, and fail to win on the first ballot.
That could result in the convention's delegates finding themselves deadlocked, forcing the party to select a compromise candidate from a list of so-called white knights.
"The process isn't sexy, but I think it's entirely possible, because it seems probable right now that no one will win on the first ballot," Matt Mackowiak, a Republican strategist and communications consultant, said Tuesday.
But brokered conventions are almost a dirty word in the United States, a signal that a party is in serious disarray in an election year, even though the Canadian-style method of choosing a party leader was commonplace stateside until the 1950s.
Historically, brokered conventions happen when there are opposing factions within a party that cannot agree on a candidate — certainly a hallmark of the 2012 Republican race.
In contemporary politics in the United States, brokered conventions allow other candidates to sweep in to take the nomination from those who have invested serious time and money in the primaries.
With Romney struggling badly on the campaign trail to hold onto his front-runner status, the calls are intensifying for a saviour to swoop in to unify the Christian evangelicals, Tea Party adherents and moderates of the party's base.
Former Indiana governor Mitch Daniels says he's being inundated with renewed pleas; so too are Jeb Bush, one-time Florida governor, and New Jersey Gov. Chris Christie.
Those close to all three men have said they're not about to throw their hats in the ring now.
One high-profile Republican has coyly signalled an interest, however: Sarah Palin.
In remarks last week, the former Alaska governor said a brokered convention was a real possibility this summer, making reference to dark-horse candidates "willing to offer themselves up...in service to their country."
She added: "I would do whatever I could to help."
Brokered conventions used to be the norm in the United States from the time of the first Democratic National Convention in 1832 right up until 1952 — the last true brokered convention held by either party.
Delegates hashed out who would lead the party in smoke-filled rooms following tense political horse-trading and backroom wheeling and dealing. Sometimes they didn't emerge with a candidate until more than 100 rounds of ballots had been taken.
Among the men who went on to win their party nominations following brokered conventions were James K. Polk, Franklin Pierce, Rutherford B. Hayes, James Garfield, Franklin D. Roosevelt, Thomas Dewey and Adlai Stevenson.
In 1952, Stevenson, the governor of Illinois, won the Democratic presidential nomination thanks to some heavy hitting from the party brass.
Former president Harry S. Truman, who didn't want to run for re-election, put Stevenson's name on the ballot and all but hand-picked him to be the party candidate.
The convention, historians say, was "brokered" in Stevenson's favour. He went on to become the nominee in both 1952 and 1956, losing each time to Republican Dwight D. Eisenhower in the presidential elections.
There were troubles at the Republican convention in 1952 as well. Most rank-and-file Republicans wanted Robert Taft, an Ohio senator, to be the party's nominee.
Taft indeed came to the convention with 800,000 more votes in Republican primaries and caucuses than Eisenhower had accumulated. But Eisenhower ended up winning the nomination at the behest of the party establishment and some powerful state governors who controlled hundreds of delegates.
Stephen Hess, a senior fellow at the Brookings Institution, was at both party conventions in 1952 in Chicago as a young student studying politics.
"That was the last time in American history when we walked into the convention hall without knowing who the nominees for either party were going to be, and it was fascinating," he said.
"It was so much fun, and how it should be, I think."
Hess doesn't believe a brokered convention is in the cards in 2012 due to stricter rules put in place by both parties and more formal nominating schedules. Those changes have served to deflate the might of the party brass.
"There's a possibility that it could go right down to the wire — Gerald Ford and Ronald Reagan came close in 1976, but Ford ended up narrowly winning on the first ballot," he recalled.
"But if we're talking about someone else emerging the way Warren Harding did in the 1920s, winning on the 10th ballot and taking the nomination? That's not going to happen."
Sean Spicer, the communications director for the Republican National Committee, has dismissed the rampant speculation about a brokered convention and a supposed white knight waiting in the wings.
"I've spent about as much time thinking about that as I have winning Powerball," he said on Tuesday on CNN.
"Who is this magical person? I think that there is satisfaction with the four candidates, they're doing a great job out there, bringing the case to the people. There are a lot of folks who sit around, thinking 'what if, what if.'"
Another possibility — and perhaps a more likely one, says Mackowiak — is a contested convention.
"That's when the remaining candidates in the race team up, partner up and cut deals," he said. "After all, in the white knight scenario, the white knight doesn't have anything to bargain with. That's not the case in a contested convention."
It's no coincidence, he adds, that Romney and libertarian congressman Ron Paul go so easy on one another on the campaign trail.
"You can already see a strong alliance between Mitt Romney and Ron Paul. It's not even a secret anymore. They're in the heavy petting stage, talking all the time, in touch a lot, being nice to each other on the campaign trail, and their wives are very friendly."
Indeed, Paul's recently released TV ad in the state of Michigan takes aim not at Romney, but at Santorum, who is ahead of the former Massachusetts governor in state polls. The commercial questions Santorum's record as a fiscal conservative, saying he voted to raise the debt ceiling five times.
Watch too, Machowiak said, for Paul and Romney to treat one another with kid gloves in Wednesday's televised debate between the four candidates in Arizona.
"I'm guessing they've got their eye on a contested convention," he said.