We did a post last month on game theory and the relationship between Trump and the GOP [emphasis added]:
However, while the relationship is simple in those terms, it is dauntingly complex in terms of the pros and cons of staying versus going. If the Republicans stand with Trump, he will probably sign any piece of legislation that comes across his desk (with this White House, "probably" is always a necessary qualifier). This comes at the cost of losing their ability to distance themselves from and increasingly unpopular and scandal-ridden administration.
Some of that distance might be clawed back by public criticism of the president and by high-profile hearings, but those steps bring even greater risks. Trump has no interest in the GOP's legislative agenda, no loyalty to the party, and no particular affection for its leaders. Worse still, as Josh Marshall has frequently noted, Trump has the bully's instinctive tendency to go after the vulnerable. There is a limit to the damage he can inflict on the Democrats, but he is in a position to literally destroy the Republican Party.
Last week, Josh Marshall made a similar point in the excellent post, Ryan Alone:
That makes the situation volatile and unpredictable. Trump's ideological commitment to this bill? Basically zero. Trump's commitment to being loved and not looking stupid? Incalculable. Trump seems at least temporarily imprinted with the access/freedom Ryan mantra. But there's every reason to think that is just skin deep. Trump may not care in any deep sense about millions of people losing their insurance coverage. But he did say his genius and deal making power would make things awesome for everyone. He wants everyone happy and loving him. This bill is not good for that agenda.