House negotiators of an immigration package are happy to let the Senate go first on the issue, saying that chamber’s proposed overhaul could serve as a useful guinea pig that improves legislation they hope to unveil in May.

The Senate’s “gang of eight” was due to file its comprehensive bill Tuesday evening, and a key Republican member of the House bipartisan immigration working group said he viewed that development positively. Rep. Raúl R. Labrador said observing how lawmakers and the public react to the group’s proposal could enable House members to adjust their bill to avoid any hurdles the Senate measure might encounter as it moves through the legislative process. (See also in Roll Call: Eight Potholes for ‘Gang of Eight’ Immigration Bill)

“It’s a good thing that [the Senate is] going to have a drafted bill,” the Idaho Republican told CQ Roll Call on Tuesday afternoon. “People can make assumptions about that bill and they can see it, they can study it, which actually will be instructive to us in the House on how to proceed.”

Labrador confirmed that the House group, which includes four Democrats and four Republicans, remains divided on some issues, even as it has reached agreements on others. A GOP source familiar with the negotiations added that some of those issues could be politically tricky to resolve. But this source predicted that the House group would ultimately reach an accord on a comprehensive immigration overhaul, and be in a position to unveil that proposal as early as May.

Bolstering the House group’s confidence is the process its members have undertaken to sell the legislation to their colleagues. Rather than guard the details of their developing proposal, the House members are seeking input from their colleagues as they write the bill, and educating them in an effort to secure broad “buy-in” for the eventual legislation. Republicans in the group have met several times with top committee leaders and members whose votes can influence others.

The GOP source said members of the House working group continue to meet with Republican members “that others look up on the board and follow,” arguing that the process is far more open than what occurred in the Senate. Meanwhile, in another signal that the House could move immigration reform in pieces rather than in a single comprehensive package, Labrador said he is advocating for “piecemeal legislation, but with a comprehensive approach.”

In recent interviews, House Chief Deputy Majority Whip Peter Roskam, R-Ill., and House Judiciary Chairman Robert W. Goodlatte, R-Va., indicated that they believe House Republicans could be more likely to support an immigration overhaul if it was legislative through multiple vehicles, as opposed to one big bill. Republicans concede that this could upset Democrats, and ultimately the decision is likely to be made by House GOP leaders. But Labrador described the process he believes would work best.

“It should be in the same week at least so people know what’s going to be voted on, so you know that you have a series of bills that are going to be going that week,” Labrador said. “And it should be done, obviously, in the right sequence so there’s assurance for both Republicans and Democrats that the things that are important to them are going to be addressed.”

Politically, momentum appears to exist in the House to clear major immigration legislation after years of opposition from both sides of the aisle.

In a possible concession from a hardline opponent that Republicans are poised to support an overhaul — at least if they can stomach the bill — Rep. Steve King, R-Iowa, didn’t appear to put much stock in his ability to generate enough opposition to kill the effort internally.

King, who emphasized that it is his “profound religious belief that we must respect the dignity of every human person,” said that only the public could exert the kind of pressure that is capable of changing minds on Capitol Hill. Recent polling has shown that most Americans support a comprehensive immigration overhaul, although self-described Republicans are less supportive than Democrats and independents.

“It’s going to be up to the American people,” King said.