I believe the possibility exists, even with the new regime. Here’s why: The Affordable Care Act has become a political quagmire for both parties. Republicans are coming to a big “Aha!” moment that there is no answer to the problem that makes good electoral sense for all of them. Any solution to the conundrum only makes good politics for some of them, while doing nothing and either allowing the ACA to continue to collapse by harassing it to death, or by simply repealing it, will be very bad for them at the next election. Meanwhile, the Democrats are stuck simply opposing the Republicans’ opposition.
If there were a “third way” that attacked the problem differently, that allowed the Republicans to say not only “we killed Obamacare” but also “See? We fixed it!” while allowing the Democrats to say, “See, we preserved healthcare access for everyone,” I think it is possible that both parties could go for it.