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Braced for big losses this year, Democrats watched the unfolding political scene with barely suppressed glee. They contend that the success of these lesser-known GOP insurgents should bolster their chances in November, despite generic polls showing voters are more likely to vote Republican than Democrat.

Instead of Mrs. Norton in Nevada, Republican primary voters chose former state Rep. Sharron Angle to run against unpopular Senate Majority Leader Harry Reid. In Kentucky, even the support of Senate Minority Leader Mitch McConnell couldn’t get Mr. Grayson past tea party favorite Rand Paul.

In Utah, incumbent Republican Sen. Robert Bennett couldn’t even make it into the two-candidate runoff, with far less well-known Mike Lee, a lawyer from Salt Lake City, emerging as the party’s candidate.

In a statement congratulating Colorado’s Mr. Bennet, Democratic Senatorial Campaign Committee chairman Sen. Robert Menendez of New Jersey said that Colorado Republicans “nominated an extremist candidate who joins the ranks of Sharron Angle, Rand Paul, and [Wisconsin businessman] Ron Johnson - all of whom are more concerned with imposing a strict social doctrine than with growing the economy.”

Not all GOP voters are betting on the underdogs. In California, Republican Meg Whitman cruised to victory in the gubernatorial primary in June, while Carly Fiorina, another party-establishment pick, won a three-way Senate primary.

In Arizona, Republican Sen. John McCain enjoys a comfortable lead over former Rep. J.D. Hayworth, whose credentials as a tea party activist and a strong voice for the party’s conservative wing haven’t translated into support in the polls.

In Florida, however, state Attorney General Bill McCollum, the party’s choice for governor, is locked a tight race with yet another newcomer, health care magnate Rick Scott.

Both Arizona and Florida hold their primaries Aug. 24.

Republicans acknowledge their hotly contested primaries may be messy - at one point, the Nevada Republican Senate primary had 11 candidates - but they also stir up voter interest. In Colorado, for example, 69,000 more Republicans than Democrats cast ballots in Tuesday’s primary election.

Mr. Bennet, in fact, received fewer votes - 183,521 - in winning against Mr. Romanoff in the Democratic race than Mrs. Norton got - 197,143 - in losing to Mr. Buck in the GOP contest. The prospect that this is a GOP year has attracted more candidates and produced spirited primary fights for Republicans in state after state.

If those primary voters stay engaged for the general election, Republicans could find themselves with a huge turnout edge, said National Republican Senatorial Committee spokeswoman Amber Marchand.

“There’s a lot of enthusiasm on our side,” she said.

If voters wind up backing primary candidates with a few rough edges, well, that’s their prerogative, she said.

“It’s the choice of the voters. They made their decision, and we’re going to be fully engaged in getting their choice elected,” said Ms. Marchand.