As I wrote earlier this month, the Wisconsin governor’s race touches a lot of national themes. On the Democratic side, it is a test of the strength of union forces that have branded Walker enemy No. 1 and a test of how effectively a candidate can be attacked for those who back him. (Walker has been supported by the Koch brothers.) But the biggest national test taking place in Wisconsin is a test of the Walker Hypothesis, which held that a politician who enacted conservative policies and didn’t shrink from the resulting controversy would be rewarded by a wide range of voters—conservatives, but also swing voters. It was a model that conservatives offered not just for other GOP governors, but for the party’s presidential candidates.

With each new poll showing a close race, that hypothesis grows weaker. Walker may win (he’s ahead by three points with registered voters, he’s an incumbent, has lots of money and is a fierce competitor) but the polls seem pretty conclusive that it will only be through a grinding and close political battle where he relies deeply on his base. That’s not how the hypothesis was supposed to work. “Results trump everything else,” Walker told National Review last November. “If you deliver, voters will stick with you,” he said during his book tour as he explained how he could capture a wide group of voters in a battleground state.

Walker may win, but the polls seem pretty conclusive that it will only be through a grinding and close political battle.