Even Wisconsin Governor Scott Walker was acknowledging Tuesday that the one million signatures that had been gathered on petitions seeking his recall and removal from office were all but certain to force him to face a new election.

Walker still thinks he will win that election.

But if he loses, and polling suggests that is a very real prospect, Walker has admitted that the anti-GOP agenda of Republican governors and presidential candidates will be dealt a blow.

Indeed, Walker suggests, Republican governors will be less inclined to attack public-sector unions. And he suggests that Democratic governors will also recognize that assaults on the rights, the benefits and the pensions of state, county and municipal employees and teachers are politically unwise.

During a recent appearance at the Reagan Ranch in California—on one of the many trips out of Wisconsin where Walker has combined addresses to right-wing groups with fund-raising pitches to wealthy conservatives—Walker was asked whether he thought pushback from unions and their allies in Wisconsin, Ohio and other states would cause Republican politicians to dial down the anti-labor rhteoric and their “battles with public employee unions.”

“I think it really largely depends on what happens in the recalls in Wisconsin—the attempt at least in the next several months against me,” Walker replied. “If somehow that was successful then I think there’s no doubt about it.”

Walker is painting his fight to save his job as a defining moment in the national wrangling over labor rights.

“If we uphold not only me but the legislative majorities in the state Assembly and state Senate in Wisconsin, even after the tens of millions of dollars thrown at our legislative candidates and against me, I think most folks [will continue taking on unions]—even those in other parties; and remember, it’s not just myself and Kasich and other Republican governors, you got even of late Jerry Brown talking about pension reform, you’ve got Andrew Cuomo talking about it in New York, you even have Rahm Emanuel, the mayor of Chicago, talking about it in the city of Chicago,” said Walker.

Wisconsin’s governor is right.

The recall fight in Wisconsin poses a threat not just to his anti-labor policies—and the cuts in public education and public services funding that go with them—but those of other politicians in both parties. If Walker is defeated in the recall election that is likely to play out this spring or summer, the signal will be recognized even in the presidential race.

The likely GOP nominee, Mitt Romney, has made attacks on labor unions central to his campaign. He is even airing anti-unions ads in South Carolina.

If Walker loses, as Ohio’s Kasich did when voters overturned his attacks on collective bargaining in last November’s referendum vote, it is hard to imagine that Romney will head into battleground states such as Wisconsin and Ohio with a union-bashing message. Even the most rigid Republican has to recognize that voters who reject a Republican governor who has already attacked labor rights would not be inclined to elect a Republican president who promises to attack labor rights.

So it is that the Wisconsin recall vote is likely to define the politics not merely of a state but a nation.