Just months ago, Senator Marco Rubio was seen by the Republican establishment as one of its best hopes for taking back the White House. Now, Representative Patrick Murphy, a second-term congressman, is within striking distance of defeating Mr. Rubio in the senator’s race to keep his seat.

The race is the most consequential among several in Florida in which Republican incumbents find themselves in unexpectedly tough fights. The plight of Florida Republicans — who seem largely resigned to a Clinton victory, given Hillary Clinton’s four percentage point lead in the polls — is in large measure a result of the name at the top of the ballot. But Donald Trump’s candidacy has only accelerated trends that have changed Florida’s political landscape in ways that Democrats have been more adept at seizing.

Representative Ileana Ros-Lehtinen, the dean of Florida’s congressional delegation, is fighting more vigorously than she ever has to fend off a Democratic challenger, Scott Fuhrman, a businessman who has little name recognition and is campaigning against Ms. Ros-Lehtinen’s rigid defense of the Cuban embargo. President Obama won the district by a tiny margin in 2008 and by nearly seven percentage points in 2012. This year, Mrs. Clinton is leading Mr. Trump by 17 to 23 percentage points in the district, according to polling commissioned by Mr. Fuhrman.

The changing Latino electorate is the key factor, with Cuban-Americans, who once swung reliably Republican, increasingly up for grabs, particularly younger voters who are more socially liberal than their parents and less dogmatic about the Cuban embargo. Some 58 percent of Latino voters in Florida back Mrs. Clinton, while 28 percent support Mr. Trump, according to a recent poll commissioned by Univision.