Far as turning tail on the AHCA goes, have to say I'm kinda curious whether the backlash from a failed vote would have been worse than what's about to hit them. Is cowardice or failure more of a trigger for the GOP base?
Withdrawing a bill shows a lack of negotiating ability on the part of the administration and House leadership/whips, disunity in the party and incompetence in drafting legislation that could attract support.
Losing a vote shows all of the above, incompetence on the part of the House leadership in letting a losing vote come to the floor, and makes all representatives put a vote on record either for or against the bill. For is for a grossly unpopular bill. Against is voting against your party and President, which usually means some form of punishment from the party and possibly their loyal base during the next election. A bill that splits the party like this (41% support among Republicans) is not a good one to vote either way on.
A vote that was lost could have easily destroyed any chance of the Republicans holding the House in 2018. It would likely have meant a serious attempt to unseat Ryan as the House leader as a proven failure, meaning more chaos and even less chance of passing anything of substance in the near future. Trump would have had fewer ways to deflect from the magnitude of the loss than he has now.
Not that this isn't going to be really ugly for them (and hugely entertaining for the rest of us) but the lost vote would have been a lot worse.
EDIT:
Basically this.House Speaker Paul D. Ryan (R-Wis.) avoided total humiliation in wriggling out of the president’s order to take what he knew would be a losing vote on the American Health Care Act. That he had to go, whip list in hand, to the White House, tells us how far he has been reduced in stature by this process.
In refusing to take a vote that apparently would not even have been close, Ryan at least avoided unnecessarily putting his own members at risk (e.g., moderates who were asked to take unpopular votes, conservatives who would disappoint the hard-edged Heritage Action and other groups working against the bill). He also retained a smidgen of his own stature. Had he gone forward he would have effectively forfeited Congress’s standing as a co-equal branch of government.
Ryan will remain speaker because no one else wants the job, but in a sense he does not “lead” the House Republicans, let alone the House. He is continuously caught in the crossfire between the moderates and the far right, just as his predecessor was. He will have his hands full keeping the House together in the future on controversial, “hard” votes. The lesson members learned was to look after their own interests. Calling Ryan and Trump’s bluff worked well for them.
While Ryan loses stature, Trump does not necessarily gain any. Previously he claimed victory merely by decimating the opposition (GOP challengers, Hillary Clinton, a reporter, etc.). Now Ryan’s loss is not Trump’s gain. (It might be Stephen K. Bannon’s gain, but not Trump, who needs to show results.) Trump shares responsibility for a bill he endorsed and lobbied hard to get. (Press secretary Sean Spicer said Trump “left everything on the field.”) His rallies and threats and his vapid cheerleading count for nothing when it comes to governance. What worked in a campaign no longer serves any useful purpose.
Trump now will rightly be seen as a weakened, if not inept, president. His attention span lasts only a couple of weeks before, starved for adulation, he moves onto the next thing in search of affirmation. Democrats know this, as do Republican opponents. You can wait this guy out.