The national spotlight has moved off of Wisconsin for the moment but a local election next week in the Badger State could provide clues about the in-state political fallout for Gov. Scott Walker (R) from the protracted budget standoff.

At stake is the post of Milwaukee County executive, which Walker held for eight years prior to being elected governor last fall. The special election to fill his vacancy is set for Tuesday.

The favorite in the race is state Rep. Jeff Stone, a Republican who took 43 percent of the vote in an open primary in mid February. Standing in his way is wealthy philanthropist Chris Abele, who finished 18 points behind Stone in the initial primary vote.

Abele’s silver bullet? Scott Walker.

Abele, who loaned his campaign $300,000 in the last seven weeks alone and has self-funded $1 million in the race to date, launched an ad today trying to link the two men.

“If you like what Scott Walker’s done then you’ll love Jeff Stone,” says the ad’s narrator. The commercial then cuts to a clip of Stone praising Walker as a “great governor” and adding that “we need someone running Milwaukee County who is going to reinforce that effort and that’s the job I intend to do”.

It’s the third ad — all of which have been produced by D.C.-based Democratic consultants John Lapp and Jason Ralston — that seeks to morph Stone into Walker. A previous ad alleged that “Jeff Stone and Scott Walker will do almost anything to stay in power” as images of the two men are flashed on screen.

Democrats insist the race is tightening although there is no public polling available to provide a sense of where the contests stands. An Abele win on Tuesday, however, will almost certainly be touted as evidence that Walker is political poison to Republicans in the state.

There is, of course, more to it.

Stone is running on his experience in office — he has spent more than a decade in the state legislature representing a district in the southwestern region of the county — while Abele is casting himself as an outsider who has never held office before. The outsider persona proved powerful in the 2010 elections as voters rejected what they believed to be status quo politicians.

Abele’s personal wealth also makes it difficult to make hard and fast conclusions about the effect the Walker attacks might be having. In the last seven-week reporting period, Abele spent nearly $650,000 on the campaign as compared to just over $200,000 for Stone, a spending disparity that could well be creating some momentum for the Democrat.

Regardless, an Abele win would strike fear in the hearts of Wisconsin Republican state senators who are facing an active effort to force recall votes on the ballot this summer and further energize organized labor nationally as they seek to push back against efforts to limit their collective bargaining rights in Wisconsin and Ohio.

Keep an eye on Milwaukee on Tuesday. It will be the first signal of how the state’s voters are dealing with the after-effects of the budget showdown.