It could happen on the Democrats’ side, Rendell says, if John Edwards remains sincere about taking his candidacy to the convention and if Hillary Clinton and Barack Obama have split the primary delegates. “Then you could go to the convention with Edwards being the balance of power.

“But remember the superdelegates,” he adds. “Those elected officials are not committed, per se, so they could fall into place before the convention for either Clinton or Obama, and that would win the day.”

A bigger chance exists for Republicans to take their primary fight into their convention if the race continues as it has, with a different winner each week.

“You could have a real possibility of four contenders going to Minneapolis," Rendell predicts. “It is probably the most significant opportunity for a brokered convention.”

Longtime Republican National Committee member Morton Blackwell of Virginia agrees that is a real possibility.

“Which means the GOP nominee could actually be decided only after delegates cast multiple ballots at the national nominating convention,” says Blackwell, a former national delegate for Barry Goldwater. “And those ballots can go into perpetuity, until a winner is decided.” Michael Barone, a senior writer at U.S. News & World Report and author of “The Almanac of American Politics,” says talk of brokered conventions is "ludicrous."

“Keep this in mind – the party that has its nominee selected ahead of time is the party that has the advantage going into the general election.”