Some big names in health care want to fix what they see as a broken system. First, they are mending fences.

Last year, a ferocious partisan battle left the Affordable Care Act, President Barack Obama's signature health law, fractured but largely intact. Andy Slavitt, a former top health official in the Obama administration, was one of the fiercest defenders of the law, rallying his nearly 200,000 Twitter followers to fight Republican efforts to overturn it.

Now, Slavitt is leading a new nonpartisan group of politicians, policymakers, executives, and other public figures—called United States of Care (USC)—that will push for policy changes based on the idea that despite deep political divisions, Americans want many of the same things when it comes to their health.