"If we keep winning races, eventually people are going to figure out that Gov. Romney is not going to be the nominee," said Santorum, eager to build on Tuesday's unexpected victories in Alabama and Mississippi.
Romney in turn dismissed Santorum as a "lightweight" as far as the economy is concerned.
He also rebutted suggestions that he can't appeal to core conservatives. "You don't win a million more votes than anyone else in this race by just appealing to high-income Americans," he said on Fox News. "Some who are very conservative may not be in my camp, but they will be when I become the nominee, when I face Barack Obama."
Romney travels to Puerto Rico on Friday, after two days in New York fundraising.
But in a reflection of the importance of next week's Illinois primary, aides announced he would make a previously unscheduled campaign stop in the Chicago area en route to San Juan.
Newt Gingrich, despite losing twice in the South, a region he hoped to own in the race, showed no sign of abandoning his fading campaign.
That presumably suited Romney fine. But not so much Santorum, eager for a race in which he is the sole challenger on the right for Romney, the former Massachusetts governor.
The events of the previous 24 hours neatly summarized the most turbulent Republican presidential campaign in a generation.
Santorum's primary victories in Mississippi and Alabama were the product of a wellspring of conservative support that overcame Romney's overwhelming organizational and financial advantages in the race to pick a November opponent for Democrat Obama.
Yet despite his twin defeats in the South, Romney remains the faraway leader in the delegate chase. Incomplete returns showed him actually adding one or two to his advantage because of overnight caucus victories in Hawaii and American Samoa.
That division -- headline-grabbing primary victories versus routine accumulation of delegates -- emerged as an increasingly significant point of contention as Romney, Santorum and Gingrich selected facts and spun theories designed to put their own hopes in the best light.
Romney's aides point out that he has more than half the delegates picked so far, and he has said he's on track to win the nomination before the party convention opens in August.
"Tuesday's results actually increased Governor Romney's delegate lead, while his opponents only moved closer to their date of mathematical elimination," said a campaign memo written during the day for public circulation.
Santorum's camp outline a strategy that relies on increasing strength in later primaries coupled with outmaneuvering Romney in caucus states where the front-runner showed early strength but delegates have yet to be picked.
"Simply put, time is on our side," the Santorum campaign said in a memo early in the week. The campaign pledged a floor fight at the Republican National Convention over the seating of winner-take-all delegations in Michigan and Florida, both of which Romney won. It also envisioned two or three rounds of convention balloting before a nominee is selected.
But it skipped lightly over Illinois, where the former Pennsylvania senator fell 10 delegates short of a full slate for the March 20 primary.
Gingrich's campaign countered with a memo Tuesday that said Louisiana's primary on March 24 is just the halfway point in the campaign and the former House speaker had succeeded in a goal of blocking "an early Romney nomination." Long gone was an earlier claim that Gingrich would be roughly even with Romney in delegates by April or May.
While the campaigns maneuvered for position, the race was on for primaries in Puerto Rico on Sunday, Illinois on Tuesday and Louisiana on March 24.
Romney's television campaign in Illinois came on top of $2.4 million that a super PAC supporting him was spending on advertising. Polls show a competitive race in that state, advantage the front-runner.
Santorum hopes to add Louisiana to his list of Southern successes, and he held his Tuesday night victory rally there.
The primary in Puerto Rico, where residents cannot vote in the fall election, is drawing unusual prominence.
Santorum met briefly with Gov. Luis Fortuno, who has endorsed Romney, and later spoke to a town hall-style audience.
He defended his decision not to try to block the promotion of Sonia Sotomayor to be a federal appeals court judge when he was a U.S. senator from Pennsylvania -- a promotion that eventually led to her nomination and confirmation as the first Latina justice on the Supreme Court. He said the Senate should allow "great deference to the president" in selecting lower court nominees and said he would expect that if he were president.
Many Republican senators voted against Sotomayor's high court confirmation in 2009. Santorum had been defeated for re-election in 2006.
With a handful of delegates yet to be allocated from Tuesday's races, the Associated Press tally showed Romney with 495 of the 1,144 needed for the nomination. Santorum had 252, Gingrich 131 and Ron Paul 46.
In a year of up-and-down turnout, Republican primary voters in Alabama and Mississippi cast ballots in record numbers.
Unofficial Alabama turnout was 621,549, topping the previous high, 554,639 in 2008, by 12 percent.
In Mississippi, unofficial turnout was 289,826, surpassing the previous high, 158,526 in 1988, by 83 percent.
In both cases, voters had an unexpectedly important role in the selection of a party nominee. It is rare for a Republican campaign to remain competitive until spring.
In this case, exit polls showed an electorate that was overwhelmingly conservative, distrustful of the federal government and eager to turn Obama out of office.
That consensus masked deep divisions when it came to sorting out the Republican field, though, and religion appeared to play a role.
Born again or evangelical voters accounted for about 80 percent of all the votes cast in Alabama and Hawaii, and Santorum picked up about 35 percent support from those voters in both states, compared with about 31 percent for Gingrich. Romney picked up 31 percent in Mississippi, the closer of the two races, but only about 27 percent in Alabama. Neither performance came close to the 38 percent support he had among evangelicals in Florida, where he was victorious.
Conservative resistance was more than a match in Mississippi for the support Romney had from the party establishment. Gov. Phil Bryant and both of the state's Republican National Committee members endorsed him.