Louisiana has not elected a Republican to the U.S. Senate since Reconstruction, so this year's GOP candidate hopes he'll make history.

But because of Louisiana's "open primary"-style election, victory is not guaranteed for GOP Rep. David Vitter (search). In Louisiana, all the candidates run against each other, and if no one gets a majority of votes, then the two top candidates have a runoff.

Louisiana Republicans are hoping Vitter can avoid a runoff election by winning more than 50 percent on Election Day. He received just under 50 percent of support in the latest polls.

Republicans think he can pull it off if he goes for broke now.

"It's certainly flattering for anybody to even say that, but I think there's going to be a runoff ... so we're focused on doing as well as we can in the primary and then going strong into the runoff," Vitter said.

The Republican is about 30 points ahead of his two closest challengers, Democratic Rep. Chris John (search) and Louisiana Treasurer John Kennedy (search), also a Democrat. The two are running within the margin of error of one another.

Louisiana is one of a handful of states where the outcome is too close to call. Political experts predict a runoff between Vitter and John.

"If there is a runoff, it will be very tight. It's the usual conservative Democrat versus a very conservative Republican and it will be very competitive," said Dr. Susan Howell of the University of New Orleans.

Click in the box near the top of this story to watch a report by FOX News' Phil Keating.