Nebraska state Sen. Deb Fischer has won the Republican nomination for U.S. Senate, setting the stage for a high-stakes November election against former Democratic Sen. Bob Kerrey.

The 53-year-old Fischer overcame low name familiarity and being outspent by two competitors to win the nomination in Tuesday's election.

She was backed by 2008 GOP vice presidential nominee Sarah Palin and former presidential candidate Herman Cain.

The race has drawn national attention because a GOP win would push Republicans closer to a Senate majority.

Nebraska is a solidly Republican state, but Democrats think they have a shot of winning with Kerrey, a former senator, governor and presidential candidate. Kerrey easily won the Democratic nomination.

The general election winner will replace Democratic Sen. Ben Nelson, who isn't seeking a third term.