And the Republican National Committee has alerted the Committee on Contests to be ready for action, preparing for the possibility of courtroomlike hearings run by lawyers that could decide whether the nomination is settled before party members take their seats in the Tampa Bay Times Forum sports arena.

The question of whether the race spills over into the convention has opened a new battleground among campaigns in the complicated system of allocating delegates in state and county party gatherings that follow the primaries and caucuses.

The process was playing out Saturday in Missouri, where Mr. Santorum urged voters to reprise his victory from a primary last month that did not allocate delegates. A caucus in St. Charles County was shut down early and the police were called when people in the crowd began chanting, “We make the rules!”

The burden of avoiding a convention fight largely rests on Mr. Romney and whether he can overcome his rivals in the pending contests.

Mr. Romney’s campaign is working intensively to stave off the possibility, especially here in Illinois in preparation for Tuesday’s primary, which it hopes to win decisively as the start of a sustained move to shut down his rivals. He beefed up his weekend campaign schedule, and he and his allies stepped up advertising to slow Mr. Santorum.

Mr. Romney has 495 of the 1,144 delegates needed for the nomination, according to a tally by The Associated Press that includes estimates of “unbound” delegates, mostly party leaders and officials who can choose which candidate to support. By the A.P. tally, Mr. Santorum has 252 delegates, Mr. Gingrich 131 and Ron Paul 48.