A Quinnipiac University poll last week, one of the first public surveys taken since the Aug. 28 primary, showed a highly competitive governor’s race. Mr. Gillum drew 50 percent from likely voters, while Mr. DeSantis was taking 47 percent. Unusually for a Republican, however, Mr. DeSantis led Mr. Gillum among Hispanic voters, 56-43 percent.

For Mr. Scott, who in two terms in office has made a concerted effort to communicate with constituencies from each Latino nationality, the advantage was even more striking: The poll showed him ahead of Senator Bill Nelson, the Democratic incumbent, by 20 percentage points with Hispanic voters.

Monday’s rally, held in a cramped room with meager air conditioning as a scrum of protesters chanted outside, was Mr. DeSantis’s first since announcing earlier in the day that he had resigned his seat in Congress retroactive to Sept. 1 to focus on the governor’s race. In a letter to Speaker Paul D. Ryan, Mr. DeSantis cited his likely absences for the rest of the congressional term as a reason to step down.

“I have to do this job because I was nominated; I think a lot of people’s hopes are riding on it. I want to do it right, and I didn’t think it was right to take a paycheck,” said Mr. DeSantis, who as a representative of the Sixth District, which includes Daytona Beach, made $174,000 a year.

Mr. DeSantis’s decision was aimed in part at denying Mr. Gillum and Democrats ammunition about his missing votes. The Republican was absent for all 14 votes on the House floor last week and likely would have missed dozens more between now and the election. Mr. DeSantis’s advisers said he would now be able to spend all of his time campaigning without having to confront criticism about wasting taxpayer money and not representing his constituents, a line of attack he implicitly sought to pre-empt in his letter of resignation.

But after being attacked in the Republican primary for being a Washington fixture who mostly communicated with Floridians via cable news interviews, Mr. DeSantis also indicated a recognition that he must further immerse himself in his state. He has proved far more comfortable discussing national issues than the more parochial topics that typically dominate governors’ races.

That includes catering to Latino voters, who comprise 16 percent of the Florida electorate. Last week, Mr. DeSantis named State Rep. Jeanette Nuñez, an experienced Cuban-American lawmaker from Miami who is well-liked in the state Capitol, as his pick for lieutenant governor. (Mr. Gillum picked Chris King, a wealthy entrepreneur from Orlando who came last in the five-way Democratic primary for governor.)