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Mr. Hatch received a bump last week when he was endorsed by tea party favorite Sarah Palin, but the endorsement prompted something of a backlash from conservatives, who have faulted Mrs. Palin for breaking with her tradition of backing underdogs who run to the right of incumbents.

“I don’t feel like Sarah Palin actually looked at his record,” said Russ Walker, national political director of FreedomWorks for America, a Washington-based tea party group that supports Mr. Liljenquist. “There’s very little difference between Orrin Hatch’s and Dick Lugar’s records.”

Meanwhile, the Liljenquist camp received a somewhat unexpected boost from Mr. Mourdock’s win in Indiana. The campaign says donations and national media coverage surged after the Lugar defeat.

There has been no independent polling released so far in the campaign, but analysts agree that Mr. Hatch is ahead - it’s just that nobody knows by how much.

“I wouldn’t bet against Hatch unless I saw several polls in succession showing him behind,” said Quin Monson, a political science professor at Brigham Young University. “Turnout in these primaries is notoriously low, but if the turnout comes from the right group, it has the potential to be very close.”