A month after House Republican leaders were forced to pull an unpopular Obamacare revision from the House floor, bill sponsor Rep. Joe Pitts, R-Pa., said he expects to see a modified version under consideration again in “a couple of weeks.”

The reworked measure appears designed to mollify critics in the rank and file who argued that the bill, as introduced, would have, in effect, just bolstered the president’s signature health care law rather than repealed its provisions.

In its original form, the bill would have taken $3.7 billion from the 2010 health care law’s Prevention and Public Health Fund and directed that money toward allowing people with pre-existing conditions to continue enrolling in high-risk insurance pools. The White House has put a moratorium on enrollment in preparation for the 2014 launch of state-run insurance exchanges that will offer such coverage.

The revamped legislation, meanwhile, would completely zero out the Prevention and Public Health Fund, Pitts told CQ Roll Call on Wednesday.

About $8.5 billion in savings incurred by repealing the fund would go toward deficit reduction, Pitts continued, and the rest would go to states to run their own high-risk pools or create new ones.

“It goes to the states. It’s under their discretion,” he said.

It could make the bill more likely to pass muster with conservative members of the Republican Conference who were under pressure from the Club for Growth and The Heritage Foundation to vote against it. The Club for Growth and The Heritage Foundation both pledged to score a vote on the original legislation, saying it improved the law rather than repealed it.

On Wednesday, Pitts emphasized that repealing the prevention fund is critical because the administration has used some of its funding to implement other parts of the law.

“They’re using it as the implementation fund for Obamacare,” he said. “Basically $54 million was taken to hire navigators to sign up people. They’re using $304 million for an advertising, media campaign on Obamacare. And they’ve used it for all kinds of other grants.”

When GOP leaders halted floor consideration on April 24, they pledged to take members’ concerns into consideration and rework some of the language to make it more palatable.

At that time, House Republican Policy Committee Chairman James Lankford, R-Okla., said he had heard from some colleagues that they had concerns with the bill helping only a certain group of people and not all those who feel threatened by the law. He also said that colleagues might be more inclined to vote for the bill if they were first able to vote on full repeal of the law.

House leadership heeded that call May 16, when it held an up-or-down Obamacare repeal vote. Meanwhile, Rory Cooper, spokesman for House Majority Leader Eric Cantor, R-Va., demurred when questioned whether this vote was intended to be an olive branch of sorts to pave the way for the high-risk pool bill to return to the floor.

In an emailed statement on Wednesday, Cooper said the revised bill would address promises made in the health care law on which President Barack Obama has reneged.

“[He] has broken many of his fundamental health care promises, including helping those with pre-existing conditions,” Cooper said. “So House Republicans remain committed to ensuring those suffering with illness and disease are helped, and not left behind by the failed Obamacare law.”