It would let states opt out of essential health benefits, a major sticking point in the inter-Republican battle over the American Health Care Act that President Donald Trump and House Speaker Paul Ryan supported.
"We don't have a bill text or an agreement, but these are the kinds of conversations we want - all the various caucus members, the administration, those productive kinds of conversations are happening right now", Ryan said.
But "if we don't get what we want, we will make a deal with the Democrats", he said.
Republicans are making healthcare reform their top priority for now, a source familiar with the agenda talkstoldReuters, after the first effort collapsed on March 24. It's unclear how they'd do that without compromising with Democrats, who now have little motivation to pull Republicans out of the quicksand.
Under the White House offer, states would be allowed to apply for waivers from several coverage requirements that President Barack Obama's 2010 health care law imposed on insurers.
After golfing with the president on Sunday, Republican Senator Rand Paul, a sharp critic of the Republicans' previous healthcare bill, also expressed renewed hope the healthcare bill could be revised in a way that picked up support from the conservative and moderate factions of the Republican Party. Yet imagine how much more intrusive, expensive, and burdensome Obamacare might have been if President Obama had been able to punish certain congressional Democrats for their reluctance to endorse a more ambitious form of health-care reform, perhaps something closer to a single-payer system. That is certainly the view of Freedom Caucus members such as Dave Brat, who said that his predecessor, House Majority Leader Eric Cantor, had "veer (ed) from the Republican creed".
Rep. Mark Meadows (NC), chairman of the House Freedom Caucus, which largely stood against the previous repeal plan because it didn't go far enough, told reporters on Monday that the plan accounts for people with high-cost coverage by allowing them to buy into risk-sharing pools.
The White House and the GOP are re-starting negotiations on a replacement to Obamacare.
"The biggest change was putting the essential health benefits back in", said Rep. Chris Collins, R-N.Y. "And, as I said, you would think even Congress should be able to put together a piece of legislation that more than 17% of our fellow citizens like". That was a requirement in Obamacare that must continue if health insurance costs are to decline for everyone.
The Trump administration is unlikely to renew its push to repeal and replace the ACA through a single bill like the AHCA, but may attempt to water down elements of healthcare reform through administrative actions created to reduce federal subsidies and weaken health insurance exchanges. Moderates did not like the cuts to Medicaid.
The day before the vote in the House, Trump and his advisers fanned out on Capitol Hill to lobby reluctant lawmakers and invited numerous them to a closed-door arm-twisting meeting in the White House before he finally issuing an ultimatum for an up or down vote.
London police charge 6 more in beating of asylum-seeker
The other two victims, Mohammed, 21, and Mustafa, 18, suffered minor injuries during the attack, the court was told. Daryl Davis and his sister, Danyelle, were slated to be released on bail along with the Potts, the girl's partner.