"Thompson's seen a precipitous decline in his standing with GOP voters over the last five months," PPP pollster Tom Jensen writes in the memo, pointing out that Thompson had 39 percent support in February and was at 29 percent in early July. "His personal image has taken a big hit as well. Where his favorability with primary voters earlier in the year was a plus-47 spread at 66/19, it's now declined 41 points to only plus-6 at 47/41."

The former governor and Health and Human Services secretary is well-known and well-liked in the state, but has been attacked for his more centrist healthcare views, including early support of an individual mandate requirement in a healthcare plan. Hovde has spent millions of dollars of his own money on the race, and Neumann has the support of the big-spending, fiscally conservative Club for Growth, which is fresh off a victory in Texas's Senate race and has run ads blasting both Hovde and Thompson.

The poll of 400 likely primary voters was conducted from July 30-31 and has a margin of error of plus or minus 4.9 percentage points.

The Hill rates this race a "toss-up," though Thompson would be the strongest general-election candidate for the GOP to face Rep. Tammy BaldwinTammy Suzanne BaldwinManaging the US dollar to pay for congressional infrastructure plans Duckworth, Pressley introduce bill to provide paid family leave for those who experience miscarriage Senate Democrats call for Medicaid-like plan to cover non-expansion states MORE (D-Wis.) in the slightly Democratic-leaning state.