SCHAUMBURG, Ill. — Backed by a crushing television ad advantage, Mitt Romney sought a strong Illinois primary victory Tuesday to solidify his lead over Rick Santorum in the battle for the Republican presidential nomination. It was the latest-in a string of must-win industrial state contests for the front-runner.

Romney held a second advantage as well, this one in the competition for Illinois delegates to the party convention next summer. Santorum was ineligible for 10 of the 54 at stake after failing to field a full slate.

Neither Newt Gingrich nor Ron Paul campaigned extensively in the state.

Romney and Santorum did, though, and not always in respectful tones.

“Senator Santorum has the same economic lightweight background the president has,” Romney said at one point. “We’re not going to replace an economic lightweight with another economic lightweight.”

Santorum had a tart reply. “If Mitt Romney’s an economic heavyweight, we’re in trouble.”

Including Romney’s victory last weekend in Puerto Rico, the former Massachusetts governor had 522 delegates going into the Illinois voting, according to The Associated Press count. Santorum had 252, Gingrich 136 and Paul 50. If Romney continues on the same pace, he will lock up the nomination before the convention opens in Tampa, Fla., next August.

However, the Santorum campaign argued Tuesday that the race for delegates is closer than that.

Santorum contends the Republican National Committee at the convention will force Florida and Arizona to allocate their delegates on a proportional basis instead of winner-take-all as the state GOP decided. Romney won both states.

As Illinois Republicans voted on Tuesday, Romney raised more than $1.3 million at a luncheon in Chicago. He planned an election-night event in nearby Schaumburg, Ill., while Santorum was in Gettysburg, Pa., site of Illinois favorite son Abraham Lincoln’s most famous speech.

Santorum, the former Pennsylvania senator, has been seeking to make up in broadcast interviews what he has lacked in advertising money.

On Monday, his campaign began before sun-up and ended well after dark, including four appearances at rallies around the state as well as an extraordinary 19 radio and television interviews. He accused Romney anew of putting his signature on a Massachusetts health insurance law that is similar to the one Obama pushed through Congress.

Romney cut short his planned time in Puerto Rico, site of a primary last weekend, to maximize his time in Illinois. He has eked out victories in other big industrial states over the past few weeks, beginning in Michigan on Feb. 28 and Ohio on March 6. Defeat in any would be likely to trigger fresh anxiety within the party about his ability to wrap up the nomination.

In Illinois, as in Michigan and Ohio, Romney enjoyed an enormous advantage in television advertising. His campaign and Restore Our Future, a super PAC that supports him, outspent Santorum and his super PAC by $3.5 million to $500,000, an advantage of 7-1.

Illinois was the 28th state to hold a primary or caucus in the selection of delegates to the nominating convention, about halfway through the calendar of a Republican campaign that has remained competitive longer than most.

A change in party rules to reduce the number of winner-take-all primaries has accounted for the duration of the race. But so has Romney’s difficulty in securing the support of the most conservative of the GOP political base. Santorum and Gingrich have struggled to emerge as the front-runner’s sole challenger from the right.

Whatever the reasons, the race appeared unlikely to end soon, with Santorum and even Gingrich vowing to campaign into the convention.

Next up is a primary Saturday in Louisiana where Santorum projects confidence following twin triumphs a week ago in Alabama and Mississippi. There are 25 delegates at stake.

Behind Louisiana is a three-primary night in the District of Columbia, Maryland and Wisconsin on April 3, with 95 delegates combined at stake.

Santorum is not on the ballot in Washington, D.C., but is ahead in opinion polls in Maryland. Wisconsin — adjacent to Illinois — shapes up as the most competitive primary of the night.