Democrat Alex Sink (AP Photo/J Pat Carter, File)

Democrat Alex Sink holds a small lead in the special election for a competitive Florida House district, according to a new poll.

The poll, from the Tampa Bay Times and Braun Research, shows Sink, the state's former chief financial officer, at 42 percent, with 35 percent going for Republican David Jolly.

Another 4 percent back Libertarian Party candidate Lucas Overby.

The poll also shows the district isn't as opposed to the federal health-care law as Republicans might hope. While 47 percent of voters oppose the law, 43 percent support it. Most national polls show that gap a little wider.

The GOP campaign so far is heavily focused on Obamacare, while Democrats have attacked Jolly as a lobbyist.

Both national Republicans and Democrats expect the race to be very close. The seat  became vacant when longtime Rep. Bill Young (R-Fla.) died.

The special election will be held March 11.