Wisconsin Gov. Scott Walker in Eau Claire, Wis. (Dan Reiland/Eau Claire Leader-Telegram via AP)

Whether they love Gov. Scott Walker (R) and the conservative agenda he drove after winning in 2010, or loathe him and voted to recall him in 2012, there’s almost no one in Wisconsin who doesn’t have a strong feeling on the subject of their incumbent governor.

Blame Walker and his legislation aimed at state employee unions, or blame Democrats for forcing a recall election and protesting in the state capitol — Walker’s first four years in office have been marked as one of the most bitterly partisan and polarizing in state history.

As he gears up to run for reelection next year, that polarization is both a blessing and a curse for Walker. Polls show he has plenty of fans, but he has so many detractors that virtually any Democrat who challenges him will start off with a strong base. Walker has a high floor, but he can’t grow much beyond a low ceiling.

Take a look at a new Marquette University Law School poll, conducted Oct. 21-24 among 800 registered voters. In the survey, Walker leads Madison School Board member Mary Burke (D) by a slim 47 percent to 45 percent margin. Walker leads Kathleen Vinehout, a Democratic state senator, by a 47 percent to 44 percent margin.

What’s striking about those numbers is how few voters are undecided, a year before Election Day. Just 6 percent said they were undecided or didn’t know for whom they would vote in the Walker-Burke matchup. Just 7 percent said the same if the contest were between Walker and Vinehout.

What stands out even more is that such a small number of Wisconsin voters actually have opinions of either Burke or Vinehout. Check out their relative favorable/unfavorable ratings:

Sixty-three percent of voters don’t know enough about Burke, and 70 percent don’t know enough about Vinehout, to say whether they have favorable or unfavorable impressions. But a sufficient number of those voters dislike Walker enough to say they’ll vote for the unknown over the known.

In most cases, voters who aren’t hard partisans and don’t know a candidate will say they’re undecided in a head-to-head matchup. Ohio is a good contrast with Wisconsin.

Earlier this year, Quinnipiac tested Gov. John Kasich (R) against both Cuyahoga County Executive Ed FitzGerald (D) and former attorney general Richard Cordray (D). Just 19 percent said they had a favorable opinion of Cordray, and 15 percent said they saw FitzGerald favorably. Kasich scored a 47 percent favorable rating.

In the head-to-head matchups, the Democrats scored a little under 20 points higher than their favorable ratings — Kasich beat FitzGerald 47 percent to 33 percent, and he outpaced Cordray 47 percent to 36 percent. A significant number of Ohio voters, around 15 percent, said they were undecided.

What’s the difference between the two polls? Why do Walker’s potential Democratic opponents do so much better than Kasich’s? (Side note: Cordray, who now runs the Consumer Financial Protection Bureau, has since said he won’t run.) Because plenty of Ohioans — 22 percent — still don’t know how they feel about Kasich.

Kasich has room to grow. Walker doesn’t. Walker has enough partisan fans that he leads his Democratic rival, but if he needs to reach out to new voters, he’ll find his audience sorely limited. As it turns out, if more than 1 million voters sign petitions to recall a governor, their opinions harden pretty quickly.

There’s a page in the political playbook for a candidate who can’t afford to see his rival improve, but who can’t grow his own support a lot either. It’s the same page Harry Reid used in 2010, along with countless other incumbents: Go negative early, and stay that way.

Get ready, Wisconsin voters, there’s an onslaught of negative advertising coming your way.