Scott Walker, the Governor of Wisconsin, is in electoral jeopardy. This may come as a surprise, because for most of 2014 he was considered an odds-on favorite for reëlection against his Democratic challenger, Mary Burke. Recent surveys show that his median lead over Burke has narrowed from seven points, at its peak, to just half a point. The Princeton Election Consortium model (of which I’m a founder)* estimates that Walker’s probability for reëlection is fifty-five per cent, which is barely better than even odds.

Walker achieved prominence in both Republican and Democratic circles when he took away collective-bargaining power from government-employee unions. This was met with angry backlash, leading to massive protests and a recall election, in 2011, which Walker survived, making him a hero to Republicans and leading some to tout him as a potential Presidential candidate. This year, Burke, the C.E.O. of Trek Bicycle Corporation, has run a campaign focussed almost entirely on being the Democratic alternative to Walker, as well as on job growth, which has been anemic in Wisconsin. The strategy—part “I’m not Scott,” part bread-and-butter policy—seems to be working.

Walker isn’t the only incumbent governor who could lose his seat. There are thirty-six gubernatorial races being held this year. This chart, from RealClearPolitics, shows elections that are competitive or likely to result in a switch.

On the left are the margins by which sitting governors won in 2010. On the right is their current performance in recent opinion polls. These incumbents are sailing into a campaign headwind. The economic recovery has been sluggish, a common feature in past gubernatorial reëlection defeats. Republicans are particularly vulnerable because they are defending gains that they made in 2010; this year, the wave has subsided a fair bit. In eight of these twelve states, voters preferred Obama or Romney by ten percentage points or less, and, in closely divided states, Democrats have been able to mount a credible challenge. Still, Democrats are not immune to the problem of governing purple states. John Hickenlooper, of Colorado, who has only a fifty per cent chance of winning reëlection, has touched several political third rails, including appearing weak on gun advocacy and the death penalty.

Economic difficulties have especially hurt the chances of three incumbents. The Democrat Pat Quinn, of Illinois, faces severe budget shortfalls, in part because of a massively underfunded public-pension system. Another Democrat, Dan Malloy, of Connecticut, also faces budget shortfalls, as well as slow economic growth. In Kansas, which is normally a reliably red state, the Republican Sam Brownback imposed deep tax cuts with no plan for how to make up for the resulting budget deficit. With no clear road to solvency for his state, Brownback is, in all likelihood, on his way out of office.

The Importance of Obamacare

The Republicans Tom Corbett, of Pennsylvania, and Paul LePage, of Maine, are both unlikely to win their races, and Nathan Deal, of Georgia, is locked in a tight contest with the Democrat Jason Carter. Corbett, LePage, Deal, and Walker have all governed according to their party’s most strongly held beliefs. They stalled or blocked implementation of the Affordable Care Act, including its Medicaid expansion. And all have sharply cut state budgets, imposing austerity measures during a recession.

To get a look at whether a Republican governor’s policy stances matter, I re-plotted some of the relevant polling data. This time, I used two symbols to represent a governor’s stance on Medicaid expansion (and other aspects of the implementation of the Affordable Care Act):

According to these data points, Republican governors who bucked their party’s stance and accepted the policy are faring better with voters—in these races, an average of 8.5 percentage points better.

Considering that crusading against Obamacare has been a core part of the G.O.P. playbook, this 8.5-point difference may come as a surprise. But it doesn’t necessarily mean that voters’ sentiments are driven entirely by health-care policy. Think of the Medicaid expansion as a “proxy variable,” one that is predictive of stands on many other issues. For example, even as Pennsylvania voters have trended toward the Democrats, Corbett got behind several radical redistricting schemes, cut education funding deeply, and compared gay marriage to incest. In Maine, LePage has called legislators idiots and state workers corrupt, told the N.A.A.C.P. to “kiss [his] butt,” and held multiple meetings with “sovereign citizens” who advocate secession. In short, if you’re too hard-core or offensive, some of your constituents can get turned off.

Who Will Survive?

The Republicans Susana Martinez, of New Mexico, John Kasich, of Ohio, and Rick Snyder, of Michigan, look as strong as they did when they were first elected. All three accepted the Affordable Care Act and its Medicaid expansion. Evidently, Obamacare is not the political liability it was once thought to be. This stance by Martinez, Kasich, and Snyder has been predictive of their support of other issues with that have drawn support from both parties. Martinez and Kasich, for example, have pursued education-reform policies that have gained a lot of traction among both Democrats and Republicans. To the extent that governors hold on to their offices in close races, it may be because they have focussed on issues that are important to the voters in their states rather than the core views of their party.

*Update: The author’s biographical information has been added to this post.