House Republicans’ plan for taking up immigration legislation is coming into sharper focus but still isn’t completely clear.

Speaker John Boehner (R-Ohio), in a July 11 press conference, stated strongly that the U.S. immigration system needs to be changed. He reiterated that the House will take up several separate bills dealing with specific immigration issues and not vote on a wide-ranging overhaul such as the one the Senate recently passed.

Boehner didn’t provide a timetable for that legislative action.

Earlier on July 11, House Minority Leader Nancy Pelosi (D-Calif.) said she supports a comprehensive immigration bill, like the one the Senate approved in June. But Pelosi said if a bill doesn’t make it through Congress this year, lawmakers aren’t likely to pass such a measure in 2014, an election year.

Neither Boehner nor Pelosi discussed a key issue for construction contractors and unions: how the House will address visas for temporary workers in construction. The Senate-passed bill includes a provision setting up a new guest-worker visa and capping the number of those visas in the construction industry at 15,000 per year.

Brian Turmail, an Associated General Contractors (AGC) spokesman, said House lawmakers are working on immigration bills that AGC expects "would be similar to the Senate's when it comes to a temporary-worker program." He adds that AGC officials "have been stressing that any such legislation should not include arbitrary caps on construction workers but have not heard whether the bills being drafted will include, or not include, such caps."

AGC expects the draft legislation will be released before the congressional August recess begins, Turmail added.

A construction union official declined comment. But organized labor has been a strong supporter of the Senate visa-cap provision, and unions are expected to oppose any anti-construction-cap proposals.

Speaking to reporters the day after House GOP members held a meeting on immigration, Boehner said, “We’ve got a broken [immigration] system. It needs to be fixed, and I made the strong case [in the meeting] that it needs to be fixed and Republicans ought to be part of the solution.”

He added, “It was clear … a vast majority of our members do believe that we have to wrestle with the problem.” He also said his GOP colleagues believe they should follow a multiple-bill, “step-by-step, common-sense approach.”