CLEARWATER BEACH, Fla. — After months of railing against President Obama’s health care overhaul, Republicans have scored a key victory in a hard-fought congressional race that has been closely watched as a bellwether of midterm elections in November.

Republican David Jolly defeated Democrat Alex Sink in a Florida special election Tuesday that largely turned on the federal health care law, with both sides using the race to audition national strategies in one of the country’s few competitive swing-voting districts.