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Mr. Pougnet — who married his longtime partner in 2008 after same-sex marriage was legalized in California but before it was banned by the ballot initiative Proposition 8 — has been mayor of Palm Springs, which has a large gay population, since 2007. He is mounting the most serious challenge yet to Mrs. Bono Mack, who for 12 years has represented the 45th District in California’s Inland Empire, a huge district that stretches from the Arizona border nearly to Los Angeles.

Mr. Pougnet had raised more than $1.2 million as of the end of June to Mrs. Bono Mack’s $1.7 million. That makes Mr. Pougnet her best-funded challenger ever. He launched his first TV ad last week in which he says Mrs. Bono Mack “isn’t getting the job done” on bread-and-butter issues such as jobs and foreclosures.

Mrs. Bono Mack has rankled members of the gay community for not opposing Proposition 8 and for voting against the repeal of the “don’t ask, don’t tell” policy on gays in the military. Her campaign manager, Ryan Mahoney, says she supports leaving gay marriage up to the states and touts the support of groups such as the Log Cabin Republicans.

Jack Pitney, a professor of government at Claremont McKenna College in California, said the district has become more Democratic in recent years and Obama carried it in 2008, but otherwise vulnerable Republicans such as Mrs. Bono Mack may be OK in a year expected to be a good one for Republicans.

But Mr. Pougnet calls it a “winnable race” and says he’s working hard to meet voters, sometimes bringing his family — he and his spouse have 4-year-old twins — to campaign events. He said his sexual orientation isn’t as important to voters as the economy, foreclosures and health care, although he’s had a lot of support from people around the country excited about the possibility of electing the first openly gay parent to Congress.

“Folks vilify gay couples with children, that somehow we’re different, and, of course, we’re not,” he said. “When folks watch us climbing the Capitol steps ready to be sworn in, America will see a family.”