House Republican leaders have scheduled a vote next week on a bill that would exclusively overturn the 2010 health care law, ostensibly to give the party’s freshman class a first chance to go on record against Obamacare.

But scheduling a vote at this time has additional advantages for GOP leaders. Allowing members to vote against the unpopular Affordable Care Act could make those freshmen more likely to support an Obamacare fix that leaders had hoped to pass on April 24.

Publicly, however, GOP leaders say their motives are altruistic.

“We’ve got 70 new members who’ve not had the chance to vote on the president’s health care law,” said House Speaker John A. Boehner, R-Ohio, at a Thursday news conference with reporters. “Frankly, they’ve been asking for an opportunity to vote on it, and we’re going to give it to them.”

But the full repeal vote certainly appears to be an attempt to offer an olive branch to the grumbling masses. Whether or not it works remains an unanswered question.

Rory Cooper, spokesman for House Majority Leader Eric Cantor, R-Va., demurred when asked specifically whether the timing was intentional or coincidental.

But House Republican Policy Committee Chairman James Lankford, R-Okla., told CQ Roll Call that he had heard from his colleagues, “especially from freshmen,” that they would feel more comfortable voting on the other bill if they were able to vote first on Obamacare’s full repeal.

That other bill would take about $3.7 billion from the Prevention and Public Health Fund to extend enrollment in the high-risk pools, which Obama put the brakes on in February.

Its critics said the bill bolstered the existing health care law rather than carve away at its provisions. Club for Growth and the Heritage Foundation weighed in as well, pledging to score any vote on the legislation.

As the number of committed “yes” votes dwindled, Republican leaders were forced to pull it off the floor after the rule providing for its consideration had been passed, saying they would take it up again some time this month.

Lankford said that while he supported the high-risk pool legislation, he understood that some Republicans were concerned that it only helped a certain group of people rather than everybody who suddenly felt threatened by the provisions of the health care law.

“Try to fix for everybody, not just a few,” was the sentiment he said he heard from GOP lawmakers.

Even if Republican leaders do decide to capitalize on the full repeal vote to try again with consideration on the high-risk pool legislation, however, there’s no certainty that its original opposition base would diminish enough to earn a majority of support.

Rep. Jack Kingston, R-Ga., the chairman of the House Appropriations’ Labor, Health and Human Services and Education Subcommittee, opposed the bill when it first came to the floor two weeks ago. Changes would have to be made for him to support it in the future, he said, adding that he didn’t think holding a repeal vote now meant that Republicans would feel automatically obliged to support that previous health-care-related legislation.

Two of the House’s more conservative lawmakers, Reps. Tim Huelskamp of Kansas and Paul Broun of Georgia, said they were looking forward to voting to overturn the health care law and it wouldn’t change how they felt about the high-risk pool bill.

“A vote for the repeal and against the expansion is the same principle,” Huelskamp said.

In the meantime, leadership has not tipped its hand on when or if the bill will come up again. Cooper said that Cantor and others continue to have conversations about the high-risk pool bill but that there isn’t currently a timetable in place for bringing the measure back to the floor.

Since Republicans took control of the House in 2011, the chamber has voted more than 30 times on amendments to or provisions contained in broader legislation that would have dismantled Obamacare.

The House in the 112th Congress also called up two bills that would, like the bill to be considered next week, do nothing but overturn the whole health care law.