The poll, conducted by Harper Polling for the Web blog Conservative Intelligence Briefing, said respondents back Enzi over Cheney, the television commentator and daughter of former Vice President Dick Cheney, 55 percent to 21 percent.
Brock McCleary of Harper Polling saidthe poll makes it "abundantly clear" Cheney "is going to have to prosecute a vigorous case against the sitting senator because the jury is skeptical at the outset that a change of representation in the Senate is needed."
The poll of 422 likely Republican voters was taken July 17-18, and has a margin of error of 4.77 percentage points.
Senate Democrats to pull all-nighter on climate change
Teacher apologizes for showing sexual image of herself in class