WASHINGTON — Congressional Republicans, stunned by their own good, if complicated, fortune, said on Wednesday that they would move quickly next year on an agenda that merges with President-elect Donald J. Trump’s, repealing the Affordable Care Act, cutting taxes, confirming conservative judges, shrinking government programs and rolling back regulations.

Like much of the nation, groggy Republicans were still trying to process results that were the opposite of what most had anticipated. Many Republicans in the House and Senate largely avoided Mr. Trump during his campaign, while a handful outright denounced him, largely to their peril. In the Senate, two incumbents and one Republican challenger who rejected Mr. Trump lost. Republicans appeared likely to secure a 52-to-48 majority in the Senate.

Mr. Trump’s victory provides what Republicans have been seeking for a decade: unified control of the government and a chance to pursue a conservative agenda, transforming them from the “party of no” into a party that can enact significant legislation.

And on Wednesday, congressional leaders said major parts of their agenda could get to the new president’s desk quickly.