When Republicans in Kentucky seized total control of the state government last year, Damon Thayer, the majority leader in the State Senate, began asking around for advice from counterparts in other capitals where the party already dominated both the legislative and executive branches.

How should we handle all this power? he wanted to know.

One answer impressed him, Mr. Thayer said, from a senior Republican lawmaker in Wisconsin: “Move quickly.”

Kentucky Republicans have done just that, swiftly passing laws to roll back the powers of labor unions and restrict access to abortion. But they are only getting started, Mr. Thayer said in an interview: They also plan to make sweeping changes to the education and public pension systems this year.

And they have plenty of company.

While Republicans in Washington appear flummoxed by the complexities of one-party rule, struggling with issues from repealing the Affordable Care Act, known as Obamacare, to paying for President Trump’s promised wall on the Mexican border, rising party leaders in the states seem far more at ease and assertive. Republicans have top-to-bottom control in 25 states now, holding both the governorship and the entire legislature, and Republican lawmakers are acting with lightning speed to enact longstanding conservative priorities.