WASHINGTON (AP) — For Majority Leader Mitch McConnell, writing a Republican-only health care bill that can pass the Senate boils down to this question: How do you solve a problem like Dean, Lisa, Patrick, Ted, Rand and Susan?

Those are some GOP senators whose clashing demands McConnell, R-Ky., must resolve. Facing solid Democratic opposition to demolishing former President Barack Obama’s 2010 over...