WASHINGTON, DC - MARCH 13: Immigrant families, some of who participated in a 3-week bus tour aimed at keeping families together, came to Captiol Hill on Wednesday demanding legislation with a path to citizenship. A large group went to the office of Senator Marco Rubio, to demand that the senator play an active role in passing immigration reform. Many immigrants spoke about their situations to a staff member. Jesus Guevara Roque, 40, right of Florida is on the left, and Rosmery Martell, 26, of DC is on the right holding her 3 month-old daughter Angie Martinez. Both of them are undocumented. (Photo by Sarah L. Voisin/The Washington Post) FILE: Immigrant families recently went to Capitol Hill demanding immigration legislation with a path to citizenship. (Photo by Sarah L. Voisin/The Washington Post)

Rep. Jeff Denham (R-Calif.) on Thursday became one of the rare House Republicans to actually speak out in favor of the Senate immigration bill.

"The Senate bill won’t get a vote in the House, and it’s something that could have helped this community,” Denham said, according to the Modesto Bee. “I am frustrated. I thought we’d get this done before the August work period. I think the Senate made tremendous progress. It was done bipartisan and I thought that would be enough to get the House moving forward.”

Denham said the reason the bill won't come to a vote "probably has a lot more to do with politics than policy."

(Hat tip to Greg Sargent for flagging the Bee's story.)

Denham is one of the few House Republicans to hail from a swing district, and it has a significant Latino population. So if anybody was going to come out in support of comprehensive immigration reform, he was a likely candidate.

The few others who have expressed support for a path to citizenship for illegal immigrants also come from competitive districts, including Reps. David Reichert (R-Wash.), Mike Coffman (R-Colo.) and Daniel Webster (R-Fla.).

These members have been the subject of significant pressure from immigration reform supporters.

So far, though, they are a small minority in the House GOP conference. Very few of Denham's House GOP colleagues -- even the vulnerable ones -- have shown a willingness to support the Senate immigration bill or a new path to citizenship.

And House Speaker John Boehner (R-Ohio) has said clearly that the House will not vote on the Senate bill, citing the so-called "Hastert Rule," which requires the support of a majority of the majority party before something comes to a vote.