As the House waits on the Senate to come up with its version of a bill to partially repeal and replace the 2010 health care law, GOP leaders on Thursday announced the chamber would move some health care bills that are part of the third phase of its overhaul strategy.

The American Health Care Act (AHCA) that the House passed in May was meant to be one of three phases of the effort because of limitations Republicans face in moving the measure through the budget reconciliation process. That process has prevented Republicans from advancing policies they typically all agree on, like allowing insurers to sell across state lines, GOP leaders have argued.

The Senate is currently debating changes to the AHCA needed to get through the divisive politics of the upper chamber, where they can afford to lose the votes of only two of the 52 Republicans, in a scenario where Vice President Mike Pence would break a tie.

Speaker Paul D. Ryan declined to say how he prefers to deal with the measure if the Senate sends it back to the House with alterations.

Ill reserve judgment on whether we go to conference or not, the Wisconsin Republican said Thursday at his weekly press conference about the health care overhaul. I just want them to pass a bill. Im really not expecting massive changes because of the reconciliation rules.

The Senate, however, is reportedly considering dropping provisions that were key to securing needed votes in the House, like the ability of states to seek a waiver to opt out of community ratings regulations, which require insurance companies to offer the same prices to everyone, regardless of their health status.

With the limitations of reconciliation, Republicans said they would advance additional health care legislation in phase three of the effort. Phase two is made up of executive actions that Human and Human Services Secretary Tom Price is undertaking to tweak the current law.

The House has already advanced a few phase three measures, and next week theyll take up more of them, House Majority Leader Kevin McCarthy said Thursday.

Specifically, he named the Veterans Act, introduced by Texas Rep. Sam Johnson, the Broader Options for Americans Act, introduced by Ohio Rep. Pat Tiberi, and the Verifying First Act, introduced by Pennsylvania Rep. Lou Barletta.

These are bills that will take 60 votes [in the Senate], that have moved out of committee here, the California Republican said.

McCarthy also announced that the House on Tuesday will take up the Veterans Affairs Accountability Act. This will actually hold VA employees accountable, it will protect the whistleblowers and it will be better care for the veterans, he said.

Looming in the background while the House works on these other measures are a number of upcoming fiscal deadlines, including the need to deal with the debt limit by late summer or early fall and to fund the government past Sept. 30, the end of the current fiscal year.

Ryan said House Republicans continue to discuss their options on both matters and have not made any decisions. He dismissed criticism that Republicans are behind

We always knew we were going to have an abbreviated budget process in this first year, like we do with every new administration, Ryan said. So were trying to figure out whats the best way to deal with our appropriations process, our budget process given the ambition [of] tax reform and savings and the constricted timetable we have.

Several House Republicans have expressed interest, given that compressed timetable, in putting together a 12-bill omnibus measure from the start and passing it by August. However, some members believe that may even be too ambitious given that the Appropriations Committee has not marked up any of the 12 bills. The first markup is scheduled for Monday on a military and veterans affairs spending bill.

On the debt limit, GOP leaders have to wrestle with how to deal with member calls for spending cuts or other overhauls to the budget process to be considered along with any increase. That pressure comes alongside a call from Treasury Secretary Steven Mnuchin for a clean debt limit free of other policy attachments, an approach Democrats have advocated for as well.

Asked if Republicans could, as a practical matter, assemble and enact a package of spending cuts with a debt limit increase by August, Ryan said, As a practical matter, the answer is 'yes,' that can be achieved. The question is, can we assemble the vote coalition and the ability to do that.

The speaker said hes not taking any options off the table in regards to the debt limit.

Were having that kind of conversation with our members about what is the best way to proceed and how can we address these fiscal deadlines we have -- budget caps needed to fix defense, debt limit, all of those things, Ryan said.

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House GOP Leaders Schedule More Health Care Votes - Roll Call