From what I can see, the Republicans have two choices when it comes to a health care system: Keep Obamacare in place, or go to a single payer system. I think we can all agree that the Republicans are not going to create a socialist single payer system, so that's leaves Obamacare as their only real option.
Obamacare really is the only sane system if you are going to keep private health insurance in place and force private companies to insure everyone at affordable rates regardless of health or income.
1. If you are going to insure sick people then you need healthy people paying into the system which requires some sort of mandate to be in the system.
2. If you are going to make it affordable, then you have to limit the amount that you charge sick people. This means having healthy people pay more.
3. If prices are too high for even the middle class (which it often is), then you need to subsidize their insurance by taxing the higher income brackets.
There is already a law in place that does all of that. It's called Obamacare. If there is one aspect of Obamacare that Republicans really hate it is the mandate to buy insurance. The people least likely to buy insurance are young and healthy people. The result is massive increases in cost for older and sick people.
This reality is probably starting to sink in within the Republican ranks. Paul Ryan made this statement recently:
We want to make sure there is an orderly transition so that the rug is not pulled out from under the families who are currently struggling under Obamacare while we bring relief.
That statement turns into pure energy due to the meeting of matter and antimatter. If people are truly struggling under Obamacare and need relief, why would they be having the "rug pulled out from under them"? It is massive contradiction.
If I were to use an analogy, I would describe the Republicans as a guy up in the stands who is yelling and screaming at the umpire in a baseball game. Suddenly, the umpire takes off all of his equipment, goes into the stands, drags the douchebag by the scruff, and then drags him down to the field. Once there, the umpire dresses him the equipment and forces him to call balls and strikes. What does the douchebag learn? It's a lot harder to umpire than it is to cry foul from the stands. That's what Republicans are suddenly learning. It's a lot harder to govern than it is to be constant douchebags that criticize every move that someone else makes.