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Democrats also are defending their Senate majority.

Republicans need to pick up a net of six seats to capture the upper chamber.

The House seat in Florida opened in October with the death of Rep. C.W. Bill Young, who served in Congress for more than four decades. The seat had been considered relatively safe as long as Young held it.

With that as a backdrop, Ms. Sink touted the need for bipartisanship on Capitol Hill and said the health care law should be fixed but not repealed.

Mr. Jolly, who was an aide to Young, countered that the law should be scrapped and tried, with the help of Young’s son, to tie Ms. Sink to House Minority Leader Nancy Pelosi, California Democrat.

The national parties and their well-heeled allies, meanwhile, dumped more than $9 million into the race, which led to a blizzard of attacks ads that left many Florida residents counting the days until the race was over.

The race played out in Pinellas County — part of the all-important “I-4 Corridor” that runs from Tampa to Orlando and is home to a deep pool of swing voters who play a key role in statewide races.

The results could bode well for Mr. Scott in his re-election push against Democrat Charlie Crist this fall.

“A Jolly win will reinforce what Republicans already believe — that six years into President Obama’s term, the best way to run and win is to highlight the public’s dissatisfaction with the president and specifically with Obamacare,” said Aubrey Jewett, political science professor at the University of Central Florida.