WASHINGTON — Republican leaders had muscled through their failure to repeal the Affordable Care Act, punted on the perennial brinkmanship over the debt ceiling and finally reached the one issue that all of the party’s factions wanted to be on, tax reform.

Then, over a Chinese dinner at the White House with the two top Democrats on Capitol Hill, President Trump threw that momentary sense of satisfaction into disarray, forcing Republicans to confront the subject that packs more emotional and political force than anything they had on their busy agenda: immigration.

Virtually nothing can drive Republicans more bitterly apart than immigration policy, which has vexed the party ever since President Ronald Reagan signed the Immigration Reform and Control Act of 1986. Republican leaders were scorched by the issue when President George W. Bush pushed it in his second term. The divisions re-emerged when President Barack Obama took it back up.

And now it re-enters the political bloodstream just when the party was desperate to demonstrate its ability to deliver on other complicated issues before lawmakers face voters next year, like lowering corporate and individual tax rates and revitalizing the nation’s infrastructure.