Nate Silver and Nate Cohn both dig into the numbers today and suggest that there’s evidence Obama may now be leading in the swing states while remaining even with or behind Mitt Romney nationally. Some of the polling models show Romney’s surge has left him narrowly ahead in national polling averages. But Cohn looks at all the polling and notes that this isn’t borne out in the battlegrounds:

On average, Romney gained 2.1 points in battleground state polls, even though he picked up an average of 5.5 points in the 11 national surveys conducted after the first presidential debate. Given Obama’s pre-debate leads in the key battleground states, a 2.1 point gain would leave Romney well short of 270 electoral votes.

Why might this be happening? Cohn suggests this explanation:

Simply put: campaigns might matter. There hasn’t been a campaign where the battleground states have endured so many advertisements for so long before the rest of the country even began to tune in. This was also a campaign where the conventional wisdom has long held that attacks on Romney did a lot of damage, especially in Ohio. While most of the country tuned in and saw Romney unadulterated by months of advertisements, voters in the battleground states might have more entrenched and cynical views of the Republican nominee.

Indeed, despite all the headlines you’re seeing this morning, the real story in today’s NBC/WSJ and NYT/CBS swing state polls is how little movement there has been in key battlegrounds, not how much. Today’s NBC/WSJ polls found that Obama leads in Ohio by 51-45, after leading by 51-43 before the debate. Obama leads in Florida by 48-47, after leading by 47-46 before the debate. Obviously, neither of those are big shifts. (The biggest movement came in Virginia, where Romney now leads by 48-47 after a shift of three points.)

Meanwhile, the NYT/CBS polls show Obama leading in Virginia by 51-46, after leading 50-46 before the debate. And Obama is leading in Wisconsin by 50-47, after leading 51-45 before the debate. Even in Colorado, where Romney now leads by 48-47, the shift was all of two points, from 47-48 before the debates.

What’s more, today’s polling also suggests perceptions of whether Romney cares about the needs and problems of ordinary people have not shifted meaningfully in Wisconsin or Virginia, and Romney’s upside-down favorability ratings have not moved much in Ohio.

Geoff Garin, the pollster for the Obama-allied Priorities USA, tells me that his polling shows that views of Romney are more fixed in the battlegrounds than nationally. “In the swing states, voters are much more apt and able to quote back the main case against Romney,” he tells me.

Garin adds that his polling has tested voter reaction to various arguments against Romney, such as the idea that his economic policies would favor the wealthy or burden the middle class. He says voter agreement with those suggestions is “higher where the advertising has occurred,” and adds: “All the swing state advertising has had a measurable and lasting impact.”

So perhaps Cohn is on to something: Obama may be doing better in the battlegrounds than he is nationally because views of Romney have hardened in these states to a much greater degree. It bears watching.