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Mitt Romney left Rick Santorum with a dwindling number of opportunities to shake up the race, at least for another month, after trouncing his chief rival in the Illinois Republican primary Tuesday.

The candidates head next into Louisiana, which votes this Saturday, and according to recent polls is leaning Santorum.

The former Pennsylvania senator said after the Illinois vote that he’s feeling “very, very good” about that race.

But after that, there are just three more contests – one of which Santorum did not qualify for – before a mid-April primary hiatus.

Romney will enter that lull boasting a sizeable delegate lead, as his campaign puts pressure on the other candidates to recognize his mathematical advantage.

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Romney won at least 41 delegates in Illinois, with Santorum winning at least 10. A total of 54 delegates were up for grabs, with the last three still undecided.

Romney now boasts 563 delegates, including endorsements from Republican National Committee members who automatically attend the convention and can support any candidate they choose. Santorum has 263 delegates, Gingrich has 135 and Paul has 50.

At his victory speech in Illinois, Romney focused squarely on the November general election.

Glossing over his rivals in the Republican contest, he described the hypothetical race between him and President Obama as a choice between a "conservative businessman" and a "law professor." Romney said "economic freedom" will be on the ballot.

"We're going to face a defining decision as a people," Romney said. "I'm offering a real choice and a new beginning."

The former Massachusetts governor stressed his private-sector experience above all else on his resume, signaling a renewed focus on jobs going into the weeks ahead. "For 25 years, I lived and breathed business and the economy and jobs," Romney said.

He said the campaign is moving closer every day to victory, as well as a "better America."

The former governor received 47 percent of the vote in Illinois, followed by Santorum with 35 percent, Ron Paul with 9 percent and Newt Gingrich with 8 percent.

Santorum, though, stressed that he would peel off some delegates from the contest. Speaking in Gettysburg, Pa., Tuesday night, he said he feels "very, very good" about Louisiana and predicted a big win a month later in his home state of Pennsylvania.

Santorum urged his supporters to "saddle up" for the race ahead, casting Romney as a flimsy conservative and himself as the candidate with "a long track record of deep convictions."

The former Pennsylvania senator took a shot at Romney, saying he doesn't fight just because of what a pollster or a teleprompter tells him. Romney used a teleprompter Tuesday night for his speech, but Santorum noted: "I don't happen to have one here tonight."

Santorum accused Romney and Gingrich of swaying with the political winds, particularly on climate change. "I'm not going to change with the climate," Santorum assured Republicans.

The candidates head next to Louisiana, where polling shows Santorum indeed has the edge -- but the state is not worth as many delegates as Illinois, with just 25 on the table. Santorum had fought hard for an Illinois upset, campaigning in the state and hoping to follow up his back-to-back wins in Alabama and Mississippi a week earlier.

Despite those wins, Santorum has struggled to make any delegate gains on Romney, who most recently added to his lead with a shutout victory in Puerto Rico over the weekend.

In Illinois, Romney invested heavily ahead of Tuesday's vote. Romney and the super PAC that supports him outspent Santorum and his super PAC by roughly 7-1 in the state, according to the Associated Press. CBS News reported the margin was 18-1, citing an estimate by the Campaign Media Analysis Group.

Operational problems in the Santorum camp also opened the door for Romney to win more delegates on Tuesday regardless of the outcome. Because of filing problems, Santorum was ineligible for 10 of the 54 delegates at stake.

Santorum adviser John Brabender, speaking to reporters before the Illinois race was called, said the nominating battle is only at about the halfway point, and projected that Louisiana on Saturday would be an "important" contest.

After that, Santorum will have to wait until late April before the state he used to represent in Congress, delegate-rich Pennsylvania, holds its primary. In between is a three-contest set in Maryland, Wisconsin and the District of Columbia on April 3, with 95 total delegates at stake. Santorum did not make the ballot in Washington, D.C., but is competitive in the other two contests.

Romney adds Illinois to a column of industrial state victories that includes Michigan and Ohio.

Exit polls in Illinois on Tuesday reflected a familiar theme. They showed Romney dominating among self-described moderates, as well as voters who view electability as the most important candidate quality. Santorum was leading among voters who most want their nominee to either have strong moral character or be a "true conservative."

Though Gingrich and Paul continue to campaign, neither campaigned extensively in Illinois.

Gingrich, in an interview on Fox News, argued that he is best suited to go up against Obama in November.

"I'm staying in the race because I really do think it's a question of who can beat Barack Obama," Gingrich said.

His campaign also put out a statement knocking Romney for spending so much in Illinois, saying, "Republicans can't nominate a candidate who relies on outspending his opponents 7-1."

Going into Tuesday's contest, Gingrich and Paul trailed in delegates -- with Gingrich at 136 and Paul at 50.

Romney had 522 delegates going into the Illinois voting, according to the AP count. Santorum had 252. It takes 1,144 to win the nomination.