Congressional supporters of Mr. Ryan describe his vote as an illustration of leadership. As chairman of the House Budget Committee, he was motivated by the chance to make the lower tax rates for most households permanent, these supporters say. And as a legislator whose actions are watched closely by fellow members, they add, he does not have the luxury of taking a purely ideological stance.

Mr. Ryan, his supporters say, did not necessarily return to the House to start building a presidential campaign. Instead, he is interested in continuing to mix things up as one of his party’s leading voices on budget matters. He is interested in forging an even tighter bond with Mr. Boehner as the fiscal fights play out, they say, starting in the coming weeks with a debate over whether to authorize raising the government’s borrowing limit and how to avoid deep across-the-board spending cuts set in motion by previous compromises…

“Paul has the long game in mind, so taking short-term pops at Boehner does not advance the conservative agenda,” an associate close to Mr. Ryan said. “He’s politically invested in his partnership with Boehner.”…

“I just don’t think 2016 is going to be litigated through the lens of this one vote,” said Kevin Madden, a Republican strategist and former adviser to Mitt Romney, “because in a month or two, we’re going to be onto a whole new deadline fight, and there will be plenty of votes and plenty of areas where you can still build your political profile and your electoral profile where you’re a viable candidate in 2016 — the full body of work so to speak.”