Former Wisconsin Gov. Tommy Thompson is not a shoo-in for the GOP Senate nomination, according to a new poll released by the Club for Growth, a group that has targeted the Republican for being too liberal.

The poll indicates Thompson is well-liked but not beloved by Republican primary voters in the state. While 68 percent of voters with a history of voting in GOP primary elections have a favorable opinion of Thompson, just 26 percent have a "very favorable" opinion of him. That compares to 61 percent "very favorable" numbers for Gov. Scott Walker (R) and 46 percent for Sen. Ron Johnson (R-Wis.).

More ominous for Thompson: He leads former Rep. Mark Neumann (R-Wis.) by just 40 percent to 34 in a head-to-head primary match-up despite his much higher name recognition. Neither Thompson nor Neumann has officially jumped into the race, although Thompson seems ready to do so.

The poll, conducted by Basswood Research, should be taken with a grain of salt, as the Club for Growth has attacked Thompson for his early support of President Obama's health insurance reform law and has indicated the organization would back a Thompson primary opponent.

Thompson now opposes the health insurance reform law, but praised many parts of it as recently as late 2009. When those polled were informed of this and other issues he supported that fall outside conservative orthodoxy, in an attempt to simulate a negative primary campaign against him, Thompson's numbers drop to 22 percent as opposed to Neumann's 40.

This does not mean Neumann would win the race should they both decide to run: The poll does not run negative questions on him, and Neumann has lost two statewide primaries against lesser-known opponents, including losing to Walker in the 2010 gubernatorial primary. But the poll does indicate that Thompson could be vulnerable in a primary should the Club for Growth decide to make him a target and a serious opponent runs.

Sen. Herb Kohl (D-Wis.) is retiring.