At the same time, the economic turnaround is not enough to raise Mr. Obama’s overall standing in several pivotal states, weighing down Democratic candidates for governor who might otherwise be in better shape.

Gov. Rick Scott of Florida, for example, was widely viewed as imperiled, but the improving economic climate in his state, where unemployment has fallen by five percentage points since Mr. Scott, a Republican, was elected in 2010, has lifted his prospects.

Governor Shumlin acknowledged the difficult climate, but expressed optimism about his party’s potential to make gains.

“In governors’ races they ask one simple question: Has the governor delivered on job growth, economic vitality and making investments in infrastructure, education and our kids’ future?” Mr. Shumlin said.

The stakes in the country’s statehouses are arguably higher than those in the battle for control of the United States Senate, which has consumed most of the media coverage and money from both parties this year. Washington is likely to remain gridlocked regardless of which party wins control of the Senate in November, but the success of Republican governors this fall, along with retention of Republican majorities in dozens of state legislatures, would cement the sweeping changes on economic and social issues that have been implemented in state capitals across the country. In 17 states with Republican governors up for re-election, the party also controls the legislature.

The state races will also have a major impact on state and national policies: the expansion of Medicaid under the Affordable Care Act, the fate of big tax cuts, and further winnowing of union rights and voting access.