Mr. Johnson wouldn’t rule out a boycott in the future if Mr. Northam stayed in office. If such a boycott developed, or if businesses in the state began to struggle financially, it could increase pressure on Mr. Northam and Mr. Fairfax to resign, and on legislators to remove them. A 2017 study found that local politicians were more likely to support removing Confederate flags from public spaces when the issue was framed as an economic concern.

Analysts said there was little reason to expect the political disarray to derail a strong state economy. Virginia came through the recession better than most states, in part because it benefited more than other places from federal stimulus spending during the downturn, and now boasts one of the lowest unemployment rates in the nation, at 2.8 percent in December. In some Washington suburbs in the northern part of the state, the unemployment rate is below 2 percent.

The state has a triple-A bond rating, a history of fiscal responsibility and a longstanding reputation for business friendliness.

“They’ve done a very good job of managing their fiscal affairs, and that’s been true across both Democratic and Republican governments for a while now,” said Eric Kim, who analyzes the state’s finances for Fitch, the bond ratings agency.

Mr. Kim noted that past controversies involving governors had not affected state economies or bond ratings. Missouri, for example, didn’t suffer economically when Eric Greitens faced a series of sex and campaign-finance scandals that led to his resignation. Even the uproar over the North Carolina “bathroom bill,” though it cost business, had only a modest economic impact on the state.

“State governments, even if there’s a controversy or turnover at the highest level, the machinery of state government continues to function,” Mr. Kim said. “Tax revenue continues to come in, and states continue to operate.”

Sure enough, Mr. Northam last week signed a bill promising tax incentives to Amazon for its planned campus in the state. He did so in private, without the public ceremony and photo opportunity that often accompany such actions. But it was nonetheless a sign that the leadership crisis hasn’t derailed the basic operations of state government.