This is an overly simplistic understanding of the government.
Why is this bill having trouble in a House controlled by the republicans?
I know why it is struggling. A lot of people HATE this bill. And I'm willing to bet even more people HATE this current bill compared to the last one.
My point is that might not matter in the end. They could still pass this bill. And if it passes in the House, it is also possible that it can pass in the Senate. And I know the odds are extremely low. But that doesn't mean the odds are zero.
No, they absolutely do care, because they want to keep getting re-elected.
The whole reason the GOP has suddenly found itself in a quagmire on healthcare is because until Trump was elected they had Obama in the White House to prevent them from acting on their promises and who could be blamed for anything that went wrong. Once they pass healthcare reform, they own the healthcare system, even moreso than they already do now with Trump in the White House.
For some many senators their states are Republican enough that it won't matter, but plenty aren't. I can give you three names right off the bat that could never vote for this bill and expect to survive: Susan Collins, Lisa Murkowski, and Dean Heller (who is up in 2018).
As I said, I know there are problems with the GOP. (I feel like I'd just say the same thing I said above. But I'm noting I saw and read this post, and do agree that there are problems in the Senate for them if it should pass the House. But I don't think the odds are zero.)