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The tea party group FreedomWorks, which was instrumental in Mr. Bennett’s defeat, ran ads against Mr. Hatch before the convention but has since limited its campaign to mailers and door-to-door efforts on behalf of Mr. Liljenquist.

FreedomWorks political director Russ Walker said that even if Mr. Hatch wins, the relentless attacks on his spending record mean that he’s likely to vote as more of a fiscal hawk than he has in the recent past. But Liljenquist spokeswoman Holly Richardson isn’t so sure.

“[Hatch] is going to be a six-year lame duck,” Ms. Richardson said. “Is he really going to change the habits he’s developed over 36 years? I doubt it. I really doubt it.”

The winner of Tuesday’s primary will face Democrat Scott Howell, a former state senator. In heavily Republican Utah, however, the winner of the Republican Senate primary is more or less guaranteed to coast to a general-election victory.