Former Wisconsin Gov. Tommy Thompson will have to win over the Republican base. (Charlie Neibergall/AP Photo)

President Obama’s health care law has become a touchstone for conservatives who see it as the most egregious example of the “government can solve our problems” mentality of the current Administration.

And, Thompson has long been a rare Republican advocate for the intent — if not the particulars — of the law.

Club for Growth President Chris Chocola blasted Thompson Wednesday afternoon, saying in a statement that the former governor “supported Obamacare” and joking that “April Fools was weeks ago” in reference to a Thompson Senate candidacy. The group followed up Thursday with a web ad attacking Thompson on the issue. Conservative talk radio hosts in the state have been throwing cold water on the prospect of a Thomson campaign as well.

“He’s opposed to Obamacare,” said Bill McCoshen, Thompson’s former campaign manager. “Nancy Pelosi and Harry Reid took health-care in a very different direction a year and a half ago, and Thompson did not support that.”

Thompson has a long series of public statements on health care that conservatives have begun to pick through.

He met with Health and Human Services Secretary Kathleen Sebelius at the White House to discuss implementation of the law. He praised various Democratic reforms in the Huffington Post. He championed the Senate Finance Committee’s health-care bill as flawed but “important progress.”

And, in a joint September 2009 op-ed with former Democratic House leader Dick Gephardt, Thompson wrote: “ Regardless of the divisive tone, Congress and the administration cannot afford to get sidetracked.” (In another joint statement with Gephardt, Thompson declared: “Failure to reach an agreement on health reform this year is not an acceptable option.”)

“I think that Tommy’s candidacy gives some conservatives some heartburn,” said Scott Becher, a Republican strategist in the state. “There’s the schism where there’s the conservatives and there’s the kind of populist Republicans.”

Thompson has problems that go beyond ideology, including a tendency towards verbal gaffes. His flirtation with the presidency in 2008 and the Senate in 2010 might have given some Wisconsin voters Tommy Thompson fatigue. He seemed to acknowledge as much when he turned down the 2010 race; “It’s time for new voices and new faces,” he said at the time.

It’s not clear who the new face would be. Former Rep. Mark Neumann is interested, but his track record is a little weak: he lost to Sen. Russ Feingold (D) in 1998 and Gov. Scott Walker in the 2010 primary. Senate Majority Leader Scott Fitzgerald and his brother, Assembly Speaker Jeff Fitzgerald, are both considering runs, although the former acknowledged recently that Thompson is “still obviously popular statewide."

That’s what Thompson supporters emphasize, saying that there’s still a lot of goodwill towards Thompson in the state, even among Democrats — something that would help in the general election if not the primary.

The question is whether that’s the approach — and tone — that Wisconsin Republicans want right now. In 2010, Walker and Sen. Ron Johnson ran closely aligned with the tea party movement — and won. Thompson’s past record — particularly on health care — could make it next to impossible for him to follow in their footsteps.