President Barack Obama met his challenger, former Massachusetts Gov. Mitt Romney, Tuesday night in Hempstead, New York, for the second of three presidential debates. CNN contributors and analysts offered these assessments of the evening:

Paul Begala: Obama capitalizes on Romney's gaffes

The Alpha Male showed up tonight.

In the second debate, President Barack Obama came. He saw. And he kicked butt.

The POTUS took command of the second presidential debate from the start. He thrashed Mitt Romney on everything from trade to taxes. And then he closed the debate by reminding everyone of Romney's arrogant assault against 47% of the American people.

When he is around real Americans, Romney is uncomfortable. He often looks like the Queen of England being forced to participate in the cow-chip tossing contest at the county fair. When asked about women in the work force, Romney, whose record of promoting women at Bain Capital was dismal, actually spoke of "binders full of women." A metaphor for the ages.

There was one "holy smokes" moment when Romney falsely accused the president of not calling the attack on our consulate in Benghazi, Libya, a terror attack. But, as the fearless and fact-based Candy Crowley noted, Romney was not telling the truth. The day after the attack, Obama referred to it as "terror" -- even before full reports were in.

Obama also shamed Romney with this exchange: Romney, whose investments at Bain Capital hurt members of the middle class, actually accused Obama of having sketchy investments. Obama nailed him to the wall, dismissing the former CEO by saying, "I don't look at my pension, it's not as big as yours, so it doesn't take that long. I don't check it that often."

Romney closed the debate by bringing up the one attack Obama left on the table: Romney's plutocratic sneer about 47% of Americans. Thank you, Mitt. Obama (finally) spanked Romney like the bad little boarding school preppy he is.

My CNN colleague Ari Fleischer called the debate a draw. Allow me to translate. When Fleischer, who is one of the great spinners of all time, calls it a draw, it's like me (a diehard Longhorn) calling Saturday's Texas-Oklahoma game a draw. I would like it to be true, but in reality, it was a butt-whipping. So was this debate.

Paul Begala, a Democratic strategist and CNN political contributor, is senior adviser to Priorities USA Action, the biggest super PAC favoring President Barack Obama's re-election. Begala was a political consultant for Bill Clinton's presidential campaign in 1992 and was counselor to Clinton in the White House.

Timothy Stanley: An Obama win to fire up Democratic base

Overall, this was an Obama win. The difference between the two men was obvious in body language. Romney walked stiffly about the stage, as if in flip flops; Obama slid across the floor like he was skating on ice. Romney was respectful and polite to the audience, but the president was far more forthright and comfortable with interjections. If anyone was playing a presidential drinking game and took a shot every time the president called someone "folks," they'd end the evening very drunk.

Obama was selling himself as a down-to-earth class warrior of the Truman variety. And while he held back in the first debate on personal attacks, this time he let it rip. He was unafraid to mention Romney's low tax rate, his U-turns on assault rifles or his apparent dismissal of the 47% of Americans who don't pay federal income taxes. The Democratic base will love this new, populist brand of Obama.

The debate was one of the most colorful on record.

We got innuendo (Mitt Romney talked about browsing through "binders full of women") and confrontations (the fight over the candidates' respective responses on Libya will surely become a classic political moment). How independents will respond to all of this, we'll have to wait to see.

My instinct is that Obama will rally among Democrats because of his commanding performance. But Romney did better when he reminded voters of high unemployment and the deficit. With one Romney win and one Obama win, the third debate seems ever more important and exciting. There's still everything to fight for.

Timothy Stanley is a historian at Oxford University and blogs for Britain's The Daily Telegraph. He is the author of "The Crusader: The Life and Times of Pat Buchanan."

Julian Zelizer: Obama bounces back; Romney stands his ground

The debate will certainly revive the spirits of Democrats. President Barack Obama came out swinging, hammering away at Mitt Romney on the budgetary costs of his program and keeping his focus on the argument that Republican policies will benefit the wealthy.

Unlike the first debate, Obama spoke with confidence, engaged his opponent and seemed comfortable with the issues that came up. Romney seemed to have more trouble with the town-hall format, sometimes early in the debate looking more aggressive than energized. Obama also finally had a chance to respond to some of the attacks on Libya that have been coming his way.

That said, Romney did not lose in the same way that Obama lost the first debate. He was able to land some blows on the president when he spoke about the laggard state of the economy and about gas prices and the deficit. He continued to remind viewers of promises that were made in 2008, and the promises that were not kept.

It is unclear that the second debate will have the same kind of impact of the first, even though it will energize Democrats and make the decision more difficult for the handful of undecided voters who are still left. The polls will remain close, the race will remain tight, and the swing states will remain the heart of this contest. That's where most people predicted this would be all along and that's exactly where it will be.

Julian Zelizer is a professor of history and public affairs at Princeton University. He is the author of "Jimmy Carter" and of the new book "Governing America."

Ilyse Hogue: Binders full of women?