California Republican Carl DeMaio raised $370,000 in the fourth quarter, another strong haul for his campaign to unseat freshman Rep. Scott PetersScott H. PetersReps introduce hurricane preparedness bill House Dems attempt to force vote on gun background checks bill Periscope shines during House blackout MORE (D-Calif.).

DeMaio, one of two openly gay Republicans who has received help from the national party, now has more than $1 million cash on hand heading into the election year.

"I'm grateful to receive this strong support, which I believe reflects both my record of getting fiscal reforms done in San Diego and my more inclusive vision for the future as a 'new generation Republican,' " DeMaio said in a statement.

DeMaio is running in a swing district he carried during his unsuccessful run for mayor of San Diego in 2012, and strategists expect a close — and expensive — race between him and Peters. Peters has yet to release his fourth-quarter fundraising numbers.

His campaign has drawn praise from a number of GOP leaders, and he's gotten fundraising support from GOP leaders, including House Majority Whip Kevin McCarthy (R-Calif.).

But there have been grumblings from some other more socially conservative Republicans over the party backing DeMaio. Rep. Randy Forbes (R-Va.) has fought against the National Republican Congressional Committee using resources to back DeMaio and other gay candidates.

DeMaio fired back against Forbes last month in an interview with The Hill. "Unlike Mr. Forbes, San Diegans aren’t focused on sexual orientation," he said.