The National Republican Congressional Committee – the fundraising arm of House Republicans – has placed a big target on Mr. Grayson, committing $817,000 for ads supporting Mr. Webster.

Yet most political experts and pollsters say the race still is too close to call. Two minor candidates, including one from the “tea party” movement, collectively are polling 9 percent and could siphon support away from Mr. Webster.

“If that doesn’t happen, Webster wins this thing,” Mr. Lee said. “For [Mr. Grayson], the anti-incumbent vote has to be split three ways, that’s the only real path to eking out a victory.”