As had been the case in past efforts, the basic approach to reform was no mystery: Everyone agreed it would involve improving border security and internal visa enforcement, rationalizing the system for legal entry and allowing most of those already here to stay. (Polls in early 2013 showed strong public support, around 70 percent, for such a package.) “The ground rules were that we wanted to come up with something that fixes the problem and can pass,” Yarmuth says. “Those were the only two criteria.”

The group was under no illusions that it would be easy to get the bill through the House. Diaz-Balart says that Boehner was all along telling him that whatever bill they came up with should ideally command a majority of Republican support, thus conforming to the Hastert rule. Getting a majority did not seem out of the question to Diaz-Balart. A small core of Republicans would be viscerally opposed to any immigration bill. But this group, by Diaz-Balart’s reckoning, was not much larger than the group firmly in favor of reform, and the great mass of House Republicans, he thought, was not out of reach.

This last group was wary of immigration — uncertain on the policy details, uncomfortable talking about it and oversensitive to the calls they got from constituents and activists opposed to it, despite the fact that very few members had ever actually been threatened over the issue by a primary challenger. But this mass operated with a herd instinct. With safety in numbers, it could potentially be moved. “Most people realize the system we have is broken,” Diaz-Balart told me.

Luis Gutiérrez was, by his own admission, not exactly a Democratic Party foot soldier when it came to immigration reform. Getting relief from the threat of deportation for families trumped all else, even party loyalty. He had been a holdout on Obamacare over the question of undocu­mented immigrants not receiving benefits and over the administration’s deferral of immigration reform — to the point of being upbraided at a meeting by Valerie Jarrett, Obama’s consigliere, who asked him why he wasn’t falling in line. “It was an intervention, and I was the drug addict,” he jokes.

In April 2013, as the Senate and House groups were plugging along with their bills, Paul Ryan joined Gutiérrez at a Chicago City Club luncheon to push immigration reform. Gutiérrez was also seeing what seemed like encouraging signs from Boehner. But he was starting to get worrisome signals from the Democratic leadership in the House, the Senate and the White House — a sense that they weren’t taking the House group’s effort seriously. They, along with reform advocates, were focusing all their attention on the Senate bill to a degree that he found nonsensical.

The R.N.C.’s Growth and Opportunity report, ordered up after Romney’s loss and released on March 18, did not mince words. “We must embrace and champion comprehensive immigration reform,” it argued. “If we do not, our party’s appeal will continue to shrink to its core constituencies only.” Democratic leaders essentially took that language at face value, assuming House Republicans were under orders to deal with the issue. They were wagering that they could get a better bill by ignoring the House group’s work; if that project failed, then the Democrats could simply press the more liberal Senate bill upon the House. “It was clear to me that no matter what I negotiated, they didn’t want me to really reach an agreement, because they wanted to go with the Senate version,” Gutiérrez says.

To Gutiérrez, this was borderline delusional; it ignored both the House’s longstanding resentment of being seen as subordinate to the Senate and the weak position of Republican leaders, whose edicts about demographic imperatives carried only so much weight with members in safe districts with few Hispanic voters. Gutiérrez told me that when he pointed out to Senate Democrats and immigrant advocates all the House Republicans who had sworn they wouldn’t accept the Senate bill, they waved off his concerns: “ ‘Don’t worry, Luis. Whatever you do, we’re going to overwhelm them with such a huge vote in the Senate’ ” — with lots of Republicans — “ ‘that they will take the Senate bill.’ It was not a plan for success.”