Updated: 11:48 p.m. ET
Facing off for the second time in the 2012 election, President Obama and Mitt Romney went head-to-head Tuesday in a spirited, wide-ranging presidential debate over which candidate would best serve the country as president -- with Mr. Obama going after Romney for what he cast as his "sketchy" economic proposals, and Romney casting Mr. Obama's presidential record as an exercise in failed promises and empty rhetoric.
Mr. Obama, whose performance in the first debate was panned as listless and dispassionate, was aggressive with his attacks right out of the gate, immediately targeting his rival for 2008 comments he made opposing the auto bailout, and for having what he called a "one-point plan" for the country: "To make sure that folks at the top play by a different set of rules."
"That's been his philosophy in the private sector, that's been his philosophy as governor, that's been his philosophy as a presidential candidate: You can make a lot of money and pay lower tax rates than somebody who makes a lot less; you can ship jobs overseas and get tax breaks for it; you can invest in a company, bankrupt it, lay off the workers, strip away their pensions, and you still make money," Mr. Obama argued. "That's exactly the philosophy that we've seen in place for the last decade. That's what's been squeezing middle class families."
The president also reiterated the critique -- cited by Democrats as well as a number of independent tax policy groups -- that the numbers don't add up in Romney's tax proposal.
Calculating what he says are the costs of implementing Romney's various proposals at $8 trillion, Mr. Obama argued that Romney hasn't been able to explain "how are you going to do it, which deductions, which loopholes are you going to close? He can't tell you."
"We haven't heard from the governor any specifics beyond Big Bird and eliminating funding for Planned Parenthood in terms of how he pays for that," Mr. Obama said. "Governor Romney was a very successful investor. If somebody came to you, Governor, with a plan that said, here, I want to spend $7 or $8 trillion, and then we're going to pay for it, but we can't tell you until maybe after the election how we're going to do it, you wouldn't take such a sketchy deal and neither should you, the American people, because the math doesn't add up."
Romney defended his tax proposal, arguing that he will not "under any circumstances, reduce the share that's being paid by the highest income taxpayers," and that his proposal, unlike the president's, will stimulate the economy and create jobs.
"And I will not, under any circumstances increase taxes on the middle-class. The president's spending, the president's borrowing will cost this nation to have to raise taxes on the American people," he added. "I want to get us on track to a balanced budget, and I'm going to reduce the tax burden on middle income families. And what's that going to do? It's going to help those families, and it's going to create incentives to start growing jobs again in this country."
He said that "of course" the numbers add up, but did not provide further information regarding the details of his proposal, pivoting instead to an attack of Mr. Obama's record.
"When we're talking about math that doesn't add up, how about $4 trillion of deficits over the last four years, $5 trillion? That's math that doesn't add up," he said. "And then we have his own record, which is we have four consecutive years where he said when he was running for office, he would cut the deficit in half. Instead he's doubled it. We've gone from $10 trillion of national debt, to $16 trillion of national debt. If the president were reelected, we'd go to almost $20 trillion of national debt. This puts us on a road to Greece."
Romney and Mr. Obama also went back-and-forth on pay equity for women, during which Romney cited calling for "whole binders full of women" when searching for qualified women to interview during his tenure as governor.
On immigration, Romney blasted the president for not having made good on his 2008 campaign promise to implement reform, and said he would implement a way to give green cards to "people who graduate with skills that we need," as well as "put in place an employment verification system and make sure that employers that hire people who have come here illegally are sanctioned for doing so."