House Speaker Paul Ryan says he's willing to bring the Senate GOP's bill to conference

House Speaker Paul Ryan said he's willing to take Senate Republicans'"skinnier" attempt at repealing certain parts of the Affordable Care Act to conference.

"If moving forward requires a conference committee, that is something the House is willing to do," he said in a statement on Thursday. That's so long as the Senate can pass the bill.

"The House remains committed to finding a solution and working with our Senate colleagues, but the burden remains on the Senate to demonstrate that it is capable of passing something that keeps our promise, as the House has already done," Ryan said.

The last-ditch, so-called skinny repeal effort would consist of a series of amendments that would aim to repeal certain unpopular parts of the Affordable Care Act, including mandates to get health insurance.

At the end of the 20-hour debate period, if no bill has been picked up, the Senate Majority Leader Mitch McConnell would move on to the "skinny repeal" plan. If passed, it could lead to the House and Senate working together to compromise on one final bill in conference.

The aim is to find common ground with the House on a bill that becomes more fleshed-out. But the House doesn't necessarily have to call a conference on the bill. It could simply pass the bill and send it to the president.

Ryan's statement might not be enough for the four GOP senators - Lindsey Graham, John McCain, Ron Johnson, and Bill Cassidy - who said they wanted assurances from House Republican leadership - including Ryan and Majority Leader Kevin McCarthy - that they would not pass the bill, which Graham called a "fraud."

The senators didn't specify what kind of assurances they would request.

"It's like pornography. You'll know it when you see it," Graham said.

The House is supposed to go into recess starting on Friday, but on Thursday, they were told to stay flexible with their travel plans.

"While last votes are currently scheduled to take place [Friday], Members are advised that - pending Senate action on healthcare - the House schedule is subject to change," McCarthy wrote. "All Members should remain flexible in their travel plans over the next few days."

Here's Ryan's full statement:

"It is now obvious that the only path ahead is for the Senate to pass the narrow legislation that it is currently considering. This package includes important reforms like eliminating the job-killing employer mandate and the requirement that forces people to purchase coverage they don't want. Still it is not enough to solve the many failures of Obamacare.

"Senators have made clear that this is an effort to keep the process alive, not to make law. If moving forward requires a conference committee, that is something the House is willing to do. The reality, however, is that repealing and replacing Obamacare still ultimately requires the Senate to produce 51 votes for an actual plan."

"The House remains committed to finding a solution and working with our Senate colleagues, but the burden remains on the Senate to demonstrate that it is capable of passing something that keeps our promise, as the House has already done. Until the Senate can do that, we will never be able to develop a conference report that becomes law. We expect the Senate to act first on whatever the conference committee produces. Obamacare is collapsing and hurting American families. We have to keep working at this until we get the job done."

What 'skinny repeal' would look like:

• The "skinny repeal" bill would repeal both the individual and employer mandates, which requires individuals to have health insurance, and employers to provide health insurance to employees. If they don't, they face a penalty fee under Obamacare.
• It would also repeal some of the taxes that the ACA put in place - most significantly, a tax on medical-device makers.
• The skinny bill would likely leave everything else untouched.
• The bill could also have some language around waiving essential health benefits, which could require the bill to get 60 votes to pass without a filibuster.

While the text of the "skinny repeal" bill hasn't been released yet, the bill would be nowhere near as extensive as the full-repeal plan or the Better Care Reconciliation Act (BCRA). But it would seek to alter the much-criticized mandates that Republicans have targeted for years.

The Congressional Budget Office scored the "skinny" plan on Wednesday and found that it would leave 16 million more Americans without health insurance.