Republicans also must decide whether to nominate troubled Gov. Jim Gibbons for a second term or choose former federal judge Brian Sandoval to oppose Democrat Rory Reid, son of the powerful U.S. senator.
The election takes place with Nevada suffering from the recession and its wake and voters divided over the direction of the nation.
Election officials predict about 25 percent of active voters will cast ballots.
The state's unemployment rate hit a record 13.7 percent in April, and Nevada leads the nation in foreclosures and bankruptcies.