The first batch of swing state polls since Mitt Romney won last week's debate show him in slightly better position in a few swing states, though the progress is not statistically significant or universal.

Here are the three new polls from NBC News and Marist College:

Virginia: Romney 48, Obama 47

Florida: Obama 48, Romney 47

Ohio: Obama 51, Romney 45

And here are the three new polls from CBS News, the New York Times and Quinnipiac University:

Colorado: Romney 48, Obama 47

Virginia: Obama 51, Romney 46

Wisconsin: Obama 50, Romney 47

The result in Florida is basically unchanged from before last week's debate. In the NBC polls, Romney gained two points in Ohio and three points in Virginia. In the CBS/NYT polls, he gained two points in Colorado and Wisconsin but lost a point in Virginia.

The good news for Romney is that his favorable rating is now in positive territory in most states. The only state showing him with a higher unfavorable rating than favorable rating is Ohio. Everywhere else, he is either in positive territory or is viewed favorably by about the same percentage who view him unfavorably.

There is good news in the polls, though, for Obama. While he might have lost some ground, the polls shows him holding relatively firm in Ohio, which is a huge state in the presidential race. No Republican has won the presidency without that state.

The Ohio poll also suggests that Obama is already building a real lead in Ohio -- i.e. actual votes. Nearly one in five poll respondents (18 percent) said they have voted early, and 63 percent of those voting early said they voted for Obama.

If that number is close to accurate, it means Obama is already building a lead in a hugely important state, which means Romney wouldn't just need to win the state on Election Day; he'd need to win it by at least a few points.