Clinton was trailing with men by 20 points; now she trails by four. She was trailing with independents, she now leads. For the past week or two, the national race has been fairly static, with Clinton enjoying about a three-point lead. (The RealClearPolitics average hasn't yet included the new CNN numbers.)

The uptick from CNN is what we'd expect to see based on the extent to which people said she won the debate. (Gallup pegged it as the third-biggest win in modern history.) But national polls don't win elections; state results do. So let's consider those, walking through the electoral college math.

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Let's start by giving Trump three states that Mitt Romney lost in 2012: Nevada, Iowa and New Hampshire. Let's assume that nothing else changes since then and that Colorado, Ohio, North Carolina, Florida and Pennsylvania are all too-close-to-call. That means Trump needs 63 electoral votes from those five states and Clinton needs 30. If we give Trump all of those states except Florida, he adds 62 electoral votes — meaning he hits 269 in total. Or, to simplify yet again: If Trump loses Florida, in this scenario, the best he can hope for is a tie.

A slew of new swing state polls came out Monday in the five states above, reinforcing the idea that Clinton's big win in the first presidential debate may have moved the contest in those states to her favor. Quinnipiac University dropped polls in Ohio, North Carolina, Pennsylvania and Florida, with Clinton leading in Florida and seeing a dramatic five-point swing in that state since the last poll, in early September. Monmouth University polled in Colorado, with Clinton holding a double-digit lead in that state.

Since the debate, the RealClearPolitics polling averages in four of the five states have moved to Clinton, to varying degrees. After the conventions, we saw bigger swings toward Clinton — though over the course of several weeks.

Again, it's the blue line on that chart that's most important to the final outcome. Clinton's lead in Florida is now bigger than her leads in Ohio or Colorado (in the polling average), which is pretty remarkable. Since Quinnipiac University's September poll, Clinton has closed the gap with Trump among men in the state by nine points while maintaining a sizable lead with women. She has gained seven points among white voters with a college degree, the swing group in the swing states.

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In Ohio, though, Clinton's position has worsened. She and Trump were tied last month, but she now trails by five points, with Trump widening the gap among men by seven points and seeing his lead with independents jump from five to 19 points. You've heard it said 100 times, but no Republican has ever won the White House without winning Ohio. (Why might Trump do so well in Ohio? Read this.) Winning Ohio, though, isn't enough to ensure victory this year.

The bigger question for Trump is how and if he can actually pass Clinton. In the RealClearPolitics average, Trump has led Clinton for only eight days this year. There have been three days this year that Trump's polling average has been above 45 percent compared with 196 days this year that Clinton has topped that mark. Trump often disparages talk about his having a ceiling, pointing to similar arguments in the primary. But in the general, he hasn't been able to manage a polling average of 46 percent in the head-to-head contest even once. In recent weeks, he has crept upward — but now Clinton's creeping along ahead of him.

The CNN-ORC poll reminds us why. Only a third of voters think Trump has the temperament to serve as president vs. Clinton. Voters see her as a stronger leader and better able to handle the job. Only a third say Trump is better prepared to handle the presidency. All of this, mind you, before the weekend revelations about Trump's taxes.