But after a humiliating defeat, which many Trump advisers are eager to pin on the speaker, Mr. Ryan is now tasked with defending not just his leadership abilities but his very brand of conservatism in a party fitfully searching for a coherent policy identity that can deliver tangible victories.

In this first fight, Mr. Ryan’s more orthodox right-leaning vision was co-opted only halfheartedly by Mr. Trump, who has few fixed political beliefs, in service of a bill the president never well understood, even as he laid on the superlatives in praising it. Now, Mr. Ryan must tug a ruptured conference toward future agenda items, like overhauling the tax code, made all the more difficult by this initial failure.

“Oh, I’m sure he’ll get blamed,” Representative Billy Long, Republican of Missouri and a vocal Trump supporter, said of the speaker as he left the Capitol on Friday, making clear he did not believe this would be fair. “He’ll get blamed for everything.”

The episode not only demonstrated an inability to honor a longstanding pledge that powered Republicans through a string of election cycles. It was also a remarkable setback for Mr. Ryan as the body’s principal arm-twister, in his first major test as the speaker under a Republican president.