Updated at 11:35 a.m.

Wisconsin Gov. Scott Walker (R) is on his way to victory in the state’s recall election tonight, but looking forward to the fall, the Obama campaign may have something positive to glean from the results.

While the totals have Walker ahead significantly, exit polls suggest he did it with a healthy dose of support from voters who are leaning toward President Obama in the fall.

In fact, exit polls show Walker winning 18 percent of Obama supporters — much higher than Democrat Tom Barrett’s 6 percent of Mitt Romney supporters. Overall, the electorate that turned out Tuesday backed Obama by a 51 percent-to-44-percent margin.

Now, all of this comes with a giant caveat; the exit polls initially were pretty far off, showing a close race between Walker and Barrett. Thus, Republicans are casting doubt that they mean much of anything at all.

“Everyone should think twice about using tonight’s Wisconsin exit polling in any fashion,” tweeted Kirsten Kukowski, a spokeswoman for the Republican National Committee.

The numbers could indeed change further, but even as the exit polls have adjusted to reflect Walker’s win, Obama’s lead has stayed. And if they are even close to accurate, Obama would have won the race with the electorate that turned out today. (We should note, however, that the electorate will be different.)

Republicans have argued that Wisconsin will be a toss-up in the fall — and the Obama campaign notably agreed with them this week, putting the race on its list of toss-ups. For now, though, it might be hard to cast Walker’s win as a big sign of GOP momentum in the presidential election.

Republicans also note that Obama won the state by 14 points in 2008, and that if Romney gains seven points on the president in most states, it would likely mean a GOP victory nationwide.

Just who are the voters who opted to keep a Republican governor, but would also return Obama to a second term in the White House?

The exit poll — a survey of 2,457 randomly selected recall voters — has barely enough such Walker-Obama to analyze. But some breakdowns are clear: 59 percent are independents, far above the rate in the overall electorate. More than half — 56 percent — described themselves as moderates, again well above the number in the full voter population. Some 52 percent are male; 23 percent are from union households.

Scott Clement contributed to this report.