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The 19th debate of the campaign season came at a pivotal time in a Republican nomination race that has featured three different winners in as many nomination contests. Mr. Santorum learned last week that he won the Iowa caucuses. Mr. Romney won the New Hampshire primary before Mr. Gingrich walked out of South Carolina victorious.

With five days to go before the Sunshine State primary, where 50 delegates and the campaign storyline are up for grabs, the debate gave the candidates an important opportunity to woo voters, including that state’s more than 450,000 Hispanic Republicans, who have brought immigration and Cuba center stage as issues.

A Romney win would help him erase some of lingering doubts over whether he’s the most electable candidate in the race. A Gingrich victory would help solidify him as the conservative alternative to Mr. Romney and give him the jolt of momentum in advance of a Feb. 22 debate in Arizona, as no candidate has taken advantage of the debate stage more than Mr. Gingrich — using them to revive his dying campaign and to help win the South Carolina primary.

Mr. Santorum, meanwhile, hopes to dig into Mr. Gingrich’s base of support. On Thursday, his campaign highlighted the ex-speaker’s drop in polls and hammered him for selling out conservative principles by previously supporting a federal health care mandate, amnesty for some illegal immigrants and Wall Street bailouts, “which is a slap in the face of the tea party.”

Mr. Paul, meanwhile, has been a relative no-show here and appears to be focusing his attention on the Feb. 4 Nevada caucuses, where he performed well in his 2008 bid.