The House is already in chaos, so resigning won't make any difference. It doesn't matter who takes over, so long as they do a better job than Ryan. All of Ryan's legislation concerning Medicare reforms etc are DOA.
Ryan should have known better than to get into bed with Trump, but then he did seem desperate to have his moment. as discussed above, apparently the Secret Freedom Caucus pact brought the whole thing down... obviously in need of a new name since they're not so secret anymore.
There is a reason why no one wanted Ryan for president. He is a tool. Trump didn't do himself any favor by not reading this law before running around endorsing it. He is, like most politicians, are too lazy to read any legislations before giving a thumb up rather, relying on people with agendas to push the laws. But do think he have learned anything from this failure? No. Rather, like a petulant child, he stomped his feet, pout, and decide to move on.....probably to his next failure.
The onus to repeal Obamacare is on the House Republicans, they've been saying it for 7 years and this was the best bill Ryan could put forth? They will be up for election in 2018. Trump knows this, he's not an idiot like most people here. Not a single one of those House Republicans will be reelected if they haven't repealed Obamacare.