House Republicans, take note: If you’ve ever hinted that you’d support a pathway to legal status for the nation’s undocumented immigrants, chances are Jeff Denham has you on his list and is coming to find you.

“I’ve got a card in my pocket of people I’m going to talk to on the floor each time I go down to vote,” the California Republican said in an interview with CQ Roll Call. “There are a lot of theories on how many Republicans we have out there. My job is to find those members.”

Denham is on a mission to prove that there’s substantial support within the House Republican Conference to move an immigration overhaul before the year’s end — one that includes a framework to provide citizenship for the millions of immigrants in the United States illegally.

It’s a contentious topic among Republicans that threatens the chances for any immigration legislation to pass the House in the 113th Congress. Influential lawmakers within the party have tried to persuade their colleagues to support an overhaul, including House Majority Leader Eric Cantor, R-Va., and Budget Chairman Paul D. Ryan, R-Wis.

They haven’t been able to provide any real momentum since the Senate passed its immigration bill in July, and there’s no guarantee that Denham will be any more successful.

But he has done something the others haven’t. On Oct. 27, Denham became the first Republican co-sponsor of a comprehensive immigration overhaul measure sponsored by 185 Democrats. An amended version of the Senate-passed bill, HR 15 is being used as a tool to “dare” GOP leaders to schedule a floor vote.

Now, Denham is daring other members to join him.

“I’d like to have half a dozen members this week and next week sign onto the bill,” Denham told CQ Roll Call in an interview Tuesday evening. “I’d like to have some real momentum as soon as we come back [from recess] so we can start scheduling hearings. And then, the first part of December, I’d like to see this on the floor.”

He may sound overly ambitious, but if his co-sponsorship was designed to create more hospitable waters for fellow Republicans, it might actually be working. On Tuesday, Rep. Ileana Ros-Lehtinen of Florida became the second GOP lawmaker to plant a flag of support for the Democrats’ bill; on Wednesday, Rep. David Valadao of California became the third.

“The more Republicans we can get on this, the more we can show that this is a bipartisan bill, the more it will elevate the issue and bring it to the floor in the short time we have left,” Denham said.

Though Denham is not new to the immigration debate, he has not actively driven the conversation before. He made his decision to come to the forefront with deliberateness, carefully controlling the rollout of his endorsement of the Democratic bill to achieve maximum exposure.

Denham’s “defining moment,” as he described it, was turning on the TV and seeing Minority Leader Nancy Pelosi, D-Calif., announce her party’s plans to introduce the Senate immigration bill in the House.

“I texted Kevin McCarthy right then,” Denham said of his longtime friend, a fellow California Republican who also happens to be the majority whip. “I said, ‘This is what I’ve been waiting to see done.’”

At that point, Denham approached Rep. Joe Garcia, D-Fla., the bill’s lead sponsor. They discussed what changes could be made, and a timeline was established for Denham to announce his endorsement. He ultimately chose to do so the second Sunday after the end of the government shutdown, on the popular Univision Sunday show “Al Punto.”

On a personal level, it makes sense that Denham would want to play a role in passing an immigration fix this year, particularly one that’s comprehensive and addresses citizenship.

With a background as an almond farmer, he’s familiar with current law’s impact on the agriculture sector; as the husband of a Latina, he helped his father-in-law navigate the system to become a naturalized citizen. And Denham’s district is 40 percent Hispanic, making immigration a hot-button issue among his constituents.

It’s also a swing district, which has left Denham with a perpetual target on his back. He is currently fighting for re-election against a formidable Democratic challenger and staving off criticism in the local press for voting against legislation to end the shutdown and raise the debt ceiling.

While Garcia, on a recent conference call with reporters, lauded Denham’s “courage” in coming out first for the immigration bill, the Democratic Congressional Campaign Committee dismissed his recent overtures as posturing.

“Congressman Denham is desperate to outrun his irresponsible record of opposing immigration reform, and his latest effort is a deathbed conversion that will be too little, too late as his leaders refuse to allow a vote on bipartisan, comprehensive immigration reform,” said DCCC spokeswoman Emily Bittner. “For Californians who have been hoping for real solutions to our country’s problems, Congressman Denham’s nakedly political efforts will fail to get the job done.”

Denham is also combating cynicism from his colleagues who say that signing onto the Democrats’ bill is a fool’s errand, and that no number of Republican co-sponsors will sway Speaker John A. Boehner, R-Ohio, to schedule a vote.

“The day I sign onto it is the day that you know that the other efforts, which are the efforts that could actually get passed, are just dead,” said Rep. Mario Diaz-Balart, R-Fla., who is actively working to introduce immigration legislation of his own. “I think [if] you ask him, he’ll probably agree that bill doesn’t have a chance of becoming law, but I think it’s a demonstration of strong support for immigration reform.”

Denham rejected suggestions of opportunism — “Whether I supported this bill or not, I would have been attacked in the district,” he said — and insisted that his conversations with leaders have made it clear to him that they want to pass some immigration bill this year.

“Who’s to say that this bill will never go to the floor?” Denham asked. “A lot of things can happen.”

Correction: 1:29 p.m.
An earlier version of this post listed the wrong state for Rep. Joe Garcia. He is from Florida.