To sway skeptical Republican lawmakers to vote this week for the House leadership's bill to repeal and replace Obamacare, Ways and Means Chairman Kevin Brady promised to move a separate bill to the House floor by the end of May that would tighten eligibility requirements for individuals who receive tax credits to purchase coverage.

The later legislation would tweak the Obamacare overhaul in other ways, too.

Hospital companies, including HCA Holdings (HCA) - Get Report , Tenet Healthcare (THC) - Get Report , LifePoint (LPNT) and Quorum Health (QHC) - Get Report  , among others, are some of the most vulnerable businesses to changes to Obamacare because they stand to see cuts in patient volume if fewer individuals are insured.

But executives at two the largest hospital firms Tuesday avoided taking sides publicly in the fight.

"While I'm not about to predict where all the repeal, replace and repair discussions will ultimately land, I want to assure you that we are actively engaged in discussions with policymakers in Washington and in our states," HCA Chairman and CEO R. Milton Johnson told analysts during the company's first quarter earnings call. "Most importantly, I'm confident HCA's long-term focus on putting the patient at the center of everything we do will serve us well no matter where these discussions may settle."

"We have a perspective about these businesses having a very permanent place in the healthcare system in the United States, probably an outcome of the legislative attempts and political rhetoric that is not as bad as many investors fear, and that it will take some time for that dust to settle," said Trevor Fetter, Chairman and CEO of Tenet Healthcare. "While we're not advocating in favor against any particular bill or legislation, we just tend to remind legislators of the importance acute care hospitals to their communities and districts, not only for providing vital emergency services and healthcare, but also as a significant source of employment, job creation."

The promise of a future vote was made to secure support for this week's legislative package from Rep. Lou Barletta R-Penn., according to Capitol Hill publication CQ.

Separate legislation is necessary because the GOP leadership is still trying to move its primary healthcare overhaul bill through Congress as budget reconciliation measure, a parliamentary maneuver that allows Senate passage with a simple 51 vote majority rather than the 60 votes typically needed to avoid filibuster from Democrats in that chamber.

Maintaining GOP support in the House has proven difficult be party conservatives and moderate are split on the extent of federal support should be provided to help lower income individuals acquire coverage. CQ said that 20 Republican lawmakers have confirmed that they oppose the GOP bill, and at least a dozen others have said they remain undecided. Given that Democrats are universally opposed to Obamacare repeal, the leadership can afford to lose only 22 Republican votes and still pass the legislation.

The moderate/conservative split caused a previous attempt to move ACA repeal and replace failed. Despite the travails, House GOP leaders are optimistic the chamber could vote on the bill as soon as this week.