It was the first contest of the year where only registered Republicans could participate, with independents and crossover Democrats restricted from casting ballots in the primary. He built a broad coalition of Republicans who found him to be the strongest candidate to take on President Obama, with exit polls showing that nearly half of the primary voters say the most important quality was someone who could defeat the president.

The outcome raised questions about Mr. Gingrich’s strength to proceed. If there was one part of Florida with a countermessage, it was in the Panhandle, which more clearly mirrors the rest of the nation’s South. Mr. Gingrich and Mr. Romney won equal support there, according to surveys of voters — giving hope to Mr. Gingrich for the a series of Southern contests on Super Tuesday, March 6, and pause to Mr. Romney, who struggled for traction in South Carolina.

After a week of intensive attack from Mr. Romney and the forces supporting him, the enthusiasm that swept Mr. Gingrich into Florida largely collapsed. Surveys of voters found that he had nearly the same percentage of strong Tea Party supporters and very conservative voters that he had in South Carolina, more than 4 in 10 — but, in a state like Florida, it was not enough to even put him close to Mr. Romney.

Representative Ron Paul of Texas finished fourth on Tuesday, his second disappointing finish in a row. But the race was moving to friendlier ground in Nevada, and he told a boisterous crowd there on Tuesday night, “We’ve only gotten started,” adding, “now the counting really occurs.”