An immigration overhaul — the most significant plank in President Barack Obama’s agenda that could see congressional action — faces its most perilous hurdle in the House.

Though many of the GOP’s power brokers in Washington, D.C., are on board, thinking that it could help Republicans make electoral inroads with Hispanic voters, the issue has proved volatile at the grass-roots level in the past.

However, since a bipartisan group of senators released an immigration framework in late January, there has been no significant backlash from the right. To the contrary, there are surprising signs of openness from key GOP lawmakers.

House leadership will obviously play an important role in how, or whether, actual legislation moves forward, as it does on any bill. But unlike most issues, the immigration landscape is surprisingly complicated. A secretive bipartisan working group is “on the cusp” of a deal, according to one of its participants. Meanwhile, a cautious, conservative Judiciary Committee chairman has been staying under the radar.

Republicans in the group include Reps. Mario Diaz-Balart of Florida, John Carter of Texas, Raúl R. Labrador of Idaho and Sam Johnson of Texas. Democrats include Reps. Luis V. Gutierrez of Illinois, Xavier Becerra of California and Zoe Lofgren of California.

While members of the group have touted its progress, House GOP leadership has been sending signals that it is interested in smaller bore legislation. For instance, Majority Leader Eric Cantor of Virginia indicated in a rebranding effort that he would support passing the DREAM Act designed to allow illegal immigrants brought to the U.S. by their parents to become citizens.

As the debate unfolds, here are five House Republicans who will prove important to whether an immigration bill gets through the chamber.

Rep. Mario Diaz-Balart, Fla.

A member of the moderate Republican Main Street Partnership group, Diaz-Balart sees his job as moving Republicans to the left. He is a longtime participant in the secretive House immigration working group, and members describe his role as talking conservatives off the ledge.

Diaz-Balart comes from a famous Cuban family and represents a Hispanic-majority district in the sprawling suburbs northwest of Miami. Elected in 2002, he is a founding member of the Congressional Hispanic Conference.

Unlike Rep. Raúl R. Labrador, Diaz-Balart praised the Senate bipartisan group’s principles as “compatible” with “discussions in the House.” But he has also sounded hawkish on securing the border in recent comments, and he is vowing not to repeat the experience of 1986, when Congress granted amnesty for millions of undocumented immigrants only to find millions more arriving in subsequent years.

Rep. Robert W. Goodlatte, Va.

On paper, the immigration issue belongs to the Virginia Republican. He’s chairman of the House Judiciary Committee, which has jurisdiction of the issue, and is a former immigration lawyer, to boot.

But there are reasons to think Goodlatte may not be as pivotal an immigration player as some of the other names on this list.

His passion isn’t immigration; it’s technology and Internet issues. Also, he rose to power by strictly following the party line, and GOP leadership is sure to have an interest in managing such a politically sensitive issue as legislation works its way through the House.

So far, he’s been extremely cautious and has openly conceded that what he does will be determined by what the rest of the GOP Conference wants. There is no evidence that the secretive working group in the House has briefed Goodlatte on its progress, although its deliberations are shrouded in mystery.

Rep. Raúl R. Labrador, Idaho

Immigration is Labrador’s chance to show bipartisan bona fides. The Idaho Republican has principally been known as a hard-line, tea party conservative. He’s of Puerto Rican heritage and is a Mormon by faith, details that only add to his unique profile.

Labrador has sternly criticized the bipartisan Senate proposal, but he is a surprising new addition to the secretive House working group on the subject. One looming question is how any proposal can square with Labrador’s public pronouncements and still garner the support of the Democrats who are participating in the talks.

If Labrador does endorse a bipartisan, comprehensive proposal from the working group, it could go a long way toward giving cover to some of the most conservative House members to support it, too. He is certainly an important voice to watch.

Rep. Steve King, Iowa

Among the most outspoken and rhetorically charged opponents of a comprehensive immigration policy rewrite, King is emblematic of the struggles Republican leaders will have in selling an immigration bill to their own party. Though King lost his spot as vice chairman of the Judiciary Subcommittee on Immigration and Border Security this year — a sign overhaul advocates took as leadership greasing the wheels for a deal — he is still likely to use his perch on the panel to push back against the legislative efforts. King has introduced bills to make English the official language of the United States and to end birthright citizenship, and he vociferously opposes a pathway to citizenship, which he sees as amnesty. He has spoken out against “open border Republicans,” and his desire to attack his own party may only increase if he ends up running in a Senate primary — especially if his opponent is Rep. Tom Latham, one of Speaker John A. Boehner’s closest friends.

Rep. Michael McCaul, Texas

As a Texas Republican and chairman of the Homeland Security Committee, McCaul will be the point man for issues related to border security that come up during the immigration debate. In fact, at a committee hearing on Wednesday, he will lay out his legislative framework for securing the border. In the past, he has backed a border fence, and though he has said comprehensive immigration changes are both possible and necessary in the 113th Congress, he believes the country must first control the southern border to stop illegal traffic. He has also called for increased Border Patrol resources and more technical steps such as deploying decommissioned drones from the Middle East Theater to the southern border. McCaul also has a close relationship with Rep. Henry Cuellar, D-Texas, which could help the GOP make inroads with the Blue Dog Coalition or the New Democrats if it needs to peel off Democratic votes for a tricky bill.