(CNN) -- Need any more evidence that debates do matter in the presidential election? A slew of national polls and surveys from crucial swing states suggests that they do.
President Barack Obama maintained a narrow lead over GOP challenger Mitt Romney in most national polls through the summer and had the advantage in battleground states that will determine the outcome of the election.
But polls taken after Obama's lackluster performance in last week's first presidential debate indicate that Romney got a measurable bounce -- enough to put him in the lead in several national surveys and to tighten the race in some battlegrounds.
The question is how long Romney's bounce will last. Thursday's vice presidential debate and the second of three presidential debates next Tuesday could answer that question.
"It's possible, even reasonable, to quibble with the likely voter sample of any individual poll, but the overall direction of the surveys released since the debate is unmistakable: They all suggest that in that debate, Romney changed a critical dynamic in the race," CNN Senior Political Analyst and National Journal Editorial Director Ron Brownstein said.
"Obama's widened lead in September depended in part on voters who were somewhat dissatisfied with his performance but were sticking with him because they did not view Romney as a viable alternative -- largely because they didn't believe he understood or cared about people like them," Brownstein added.
"What's clear is that at the first debate Romney crossed the threshold for an important share of those voters, who now do see him as a reasonable alternative to Obama," he added.
Let's start with the national surveys.
According to a CNN Poll of Polls that averages three new non-partisan, live-operator surveys released Monday and Tuesday, Romney has the support of 48% of likely voters, with Obama at 47%.
The surveys were from the Pew Research Center, which conducted its poll Thursday through Sunday (entirely after the debate); the American Research Group, which conducted its poll Friday through Monday (entirely after the debate); and the Gallup Daily Tracking Poll, which was conducted from last Tuesday through Monday (partially before and mostly after the debate).
The Gallup daily tracking poll indicated Romney at 49% and Obama 47% among likely voters. This is Gallup's first release of a tracking poll of likely voters, so no comparison can be made to pre-debate surveys from Gallup.
The ARG poll indicates the former Massachusetts governor at 48%, with Obama at 47%. According to ARG's previous poll, conducted Sept. 27-30, the president was at 49% and Romney at 46%.
The Pew Poll indicates Romney with a 49%-45% advantage over Obama. In Pew's previous survey, conducted in mid-September, the president had a 51%-43% lead among likely voters.
While national polls serve as a barometer, the race for the White House is a battle for the states and their electoral votes, which is why surveys in the key swing states are more telling. And no state arguably is getting more attention from the presidential candidates and their campaigns than Ohio, where 18 electoral votes are up for grabs.
According to a CNN/ORC International poll, 51% of likely voters in the Buckeye State say they're backing Obama, with 47% supporting Romney. Obama's four-point advantage is within the poll's sampling error.
The survey, released Tuesday, was conducted from Friday through Monday. ARG also came out Tuesday with an Ohio poll conducted entirely after the debate that indicated Romney at 48% and Obama at 47% among likely voters.
Since non-partisan, live operator polls of likely voters in Ohio conducted prior to the debate indicated Obama with a seven- to 10-point advantage, the polls suggest that Romney got a post-debate bounce in Ohio, too.
"The new polls are a huge boost for Republicans, coming just a couple weeks after a string of polls made them wonder if there was any way to win without Ohio," says CNN Chief National Correspondent John King.
"There is clearly movement in Ohio similar to what we see nationally. You see it in our numbers. It's a very close race in Ohio and you feel it talking to people on the ground," King added.
Republican Sen. Rob Portman said he had expected to polls to tighten up in his home state.
"The poll numbers are showing some movement. But you know I've always thought this was going to be a very close race in Ohio," he told reporters on Tuesday.
Portman is a leading Romney surrogate and a top adviser to his campaign. Portman is also playing the role of Obama in Romney's debate preparations. Asked if Romney is sensing enthusiasm, Portman said, "Yeah, I think so."
But earlier Tuesday, Romney campaign spokesman Kevin Madden cautioned that "this is a campaign that's never gotten too high when things are good, too low when things are bad," adding that "we still believe that this is going to be a campaign that's very close."
Polls show a similar bounce in other battlegrounds.
A new ARG poll in Colorado indicates Romney with a 50%-46% advantage. That's a switch from last month, when surveys in the Rocky Mountain battleground state indicated Obama with a slight edge.
Last month polls in Michigan indicated the president with a healthy lead but an EPIC-MRA survey released Monday showed his advantage had slipped to 48%-45%.
And new polls in New Hampshire and Pennsylvania, where Obama held leads last month, now suggest much closer contests.
With this week's vice presidential debate and two more showdowns between Obama and Romney still to come, the polls can quickly shift again. But the new numbers this week suggest the race has changed.
"The new polls don't mean Romney is going to win, or is even ahead today if it was possible to precisely measure that. But they do mean that we are returning to a race that reflects the country's near 50-50 division over Obama's performance and, as such, is likely to remain close and within reach for both men through November," Brownstein said.