LAS VEGAS — It was over 100 degrees here the other evening, but inside a buzzing office tucked away on a stretch of gun stores and pornography shops, Democrats were staring into computer screens and talking urgently into cellphones. The stakes were high: The Nevada Senate, which Democrats control by a single seat, could very well shift into Republican hands after November.

“Hi, this is Justin Jones; I’m your state senator,” said Mr. Jones, a Democrat who won by only 301 votes two years ago. “We have a really important election campaign coming up this fall. I wanted to see if I could count on your support.”

Pause.

“Great, Ronald, that’s fantastic.”

It is not only Nevada. Republicans, who had appeared to hit a high-water mark in control of statehouses in recent years, are seeking to pick off another half-dozen chambers this year, taking advantage of President Obama’s persistent unpopularity, anxiety about the economy, and a history of anemic turnout among Democrats in nonpresidential election years. In addition, the party that controls the White House almost always loses seats in statehouses in those years.

At a time when Democrats and Republicans in control of statehouses are using their authority to push through ambitious policies that by contrast highlight the paralysis in Washington, the potential for further Republican gains has raised the possibility of deepening the policy divide between red and blue states. Republicans now control 59 of the 98 partisan legislative chambers, and have complete political control — both legislative houses and the governor’s mansion — in 23 states, while Democrats control 13. The total number of states ruled by a single political party, 36, is the highest in six decades.