A number of House conservatives are unhappy with the Republican leadership’s decision to allow for the passage on Thursday of a Senate-passed reauthorization of the Violence Against Women Act.

After spending weeks hashing out their own proposal, House GOP leaders abruptly switched course and decided to approve a process to hold a vote on the Senate bill if their own version failed to pass. The two measures contained significant overlap but differed on a contentious issue affecting tribal courts.

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The move likely means that for the third time in the last two months, the House will pass a significant piece of legislation with minority Democrats carrying the vote.

“It’s a huge concern,” Rep. Raul Labrador (R-Idaho) told reporters at a conservative press event Tuesday. He and other members were particularly worried, he said, that the House accepting bills from the Senate without moving a Republican version was “becoming the norm.”

On New Year's Day, the House passed legislation on the fiscal cliff that a majority of Republicans opposed. And weeks later, GOP leaders watched as most of the conference voted against a Democratic-supported bill providing relief for states damaged by Hurricane Sandy.

Labrador said he did not necessarily oppose the Violence Against Women Act (VAWA) but that members believed the House should have sent its own version through the regular committee process.

“It should go through regular order,” he said. “It should have gone through the Judiciary Committee. It should have gone through the subcommittee. I don’t understand what aversion we have to actually going to through regular order.”

“I know there’s a lot of people that are upset about the process, not necessarily the language of the bill or anything like that,” Labrador said.

Reps. Steve King (R-Iowa), Tim Huelskamp (R-Kan.) and Matt Salmon Matthew (Matt) James SalmonCOVID-19's class divide creates new political risks Arizona voters like Kyl but few think he'll stick around Former Sen. Jon Kyl to replace McCain in Senate MORE (R-Ariz.) all indicated they may vote against a procedural motion on Wednesday that governs debate on final vote, which is expected Thursday.

King said he voted against a similar motion, known as the rule vote, last year when the leadership replaced a version of the VAWA that had gone through the Judiciary Committee with a new alternative.

“I intend to do so this time, to send a message to send this back through regular order,” King said. “This House can only work its will if we use the committees and misses out on a lot of the input we would have if we worked it through regular order.”

The leadership’s shift means that after a year of bickering between the House and Senate over the measure, the Senate legislation, which passed on a bipartisan vote, could reach President Obama’s desk by the end of the week.

“They figured out they didn’t have the votes” on the Republican measure, a GOP aide said.

The issue underscores the difficulty Speaker John Boehner John Andrew BoehnerLongtime House parliamentarian to step down Five things we learned from this year's primaries Bad blood between Pelosi, Meadows complicates coronavirus talks MORE (R-Ohio) has had in navigating between pressure from conservatives on his right and the White House and Senate Democrats on his left.

He has recommitted to the regular order process in the new Congress, but he has also told Republicans that the party must pick its battles with the “Democratic majority” in Washington. Democrats have been hammering Republicans for months over the bill after Obama won big with women voters in the November election.