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Mr. Gingrich shrugged off the result, arguing that the party shouldn’t pin their hopes on a candidate who depends on outspending his foes to win.

“Instead, we need a nominee who offers powerful solutions that hold the president accountable for his failures,” he told Fox News, claiming that his proposal to drive gas prices down to $2.50 a gallon has put the White House on their heels.

“This is the type of leadership I can offer as the nominee, and this campaign will spend between now and when the delegates vote in Tampa relentlessly taking the fight to President Obama to make this case,” the former House speaker said.

Mr. Gingrich was campaigning in Louisiana and Mr. Paul, who made one stop here last week, also plans to head to that state.

Mr. Romney led consistently in the polls in the days before the Illinois vote, but Mr. Santorum held out hope that he could pull an upset and reinforce doubts about Mr. Romney’s strength in a head-to-head matchup with Mr. Obama.

A Chicago Tribune poll this month showed Mr. Santorum within 4 points of Mr. Romney. But since then, despite his headline-grabbing victories in the Alabama and Mississippi primaries last week, the former senator from Pennsylvania has seen his stock drop while Mr. Romney’s lead has risen.

The Santorum campaign didn’t help itself with its failure to fill out full delegate slates in all of the state’s 18 congressional districts. As a result, Mr. Santorum was eligible to collect at most 44 delegates, while the rest of the field is eligible for all 54.

Political pundits said low voter turnout could have been problematic for Mr. Romney and beneficial for Mr. Santorum, who has had a much easier time connecting with self-identified “very conservative” voters, evangelical or born-again Christians and those who identify with the tea party movement.

Mr. Romney’s success, meanwhile, has largely been driven by voters who are attracted to his business background and the sense that he presents Republicans with the best chance of knocking off Mr. Obama in a general election.

Exit polls showed that Mr. Santorum outperformed Mr. Romney again among self-identified evangelical and born-again Christians, but those voters constituted a much smaller slice of the electorate.

Mr. Romney, meanwhile, won among those who “strongly support” the tea party movement — something he didn’t do in either of the Deep South primaries last week.

As usual, Mr. Romney had the upper hand on the airwaves.

The Associated Press reported Tuesday that his campaign and Restore Our Future, the super PAC that supports him, outspent the Santorum campaign, and the super PAC aligned with him, $3.5 million to $500,000.

The advantage was clear, as Mr. Romney flooded the state with television commercials. In one, Mr. Santorum was described as an “economic lightweight” — a catchphrase that has become a go-to attack for the Republican front-runner.

“Who can turn around the economy and defeat Barack Obama? Not Rick Santorum,” the ad’s narrator says.

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