RALEIGH, N.C. — When Republicans took control of virtually every lever of North Carolina’s state government for the first time since Reconstruction, they set out to transform the historically moderate Southern state into a more conservative stronghold.

That was less than seven years ago.

These days, the question is how much Republicans may have set their project back with a recent string of remarkable self-inflicted wounds.

“It’s never a dull moment with the Republicans here,” said Morgan Jackson, a Democratic strategist and an ally of Gov. Roy Cooper, the Democrat whose November 2016 election was helped along by the protracted fight over a Republican-backed bill limiting the bathroom choices of transgender people. “Every time we think it can’t get worse, they figure out a way to dig deeper.”

This week, federal prosecutors announced that the chairman of the state’s Republican Party, Robin Hayes, had been indicted on charges of bribery and other crimes related to a scheme they said was designed to aid a major donor, who was also charged. The revelation came almost six weeks after Republicans faced the rare embarrassment of watching their seeming victory in a congressional race unravel after it became clear that their nominee had financed an illicit voter-turnout effort.