WASHINGTON (AP) -- President Barack Obama and Republican Mitt Romney teed up the last three weeks of the presidential election as a question of which man voters can trust to improve the economy.
If the undecided voters who questioned the two men in Tuesday's fast-paced debate are an indication, then the Nov. 6 contest may turn on whether like-minded Americans decide to stick with a disappointing-but-progressing president, or gamble on a challenger who swears he knows how to create jobs, but provides few details to shore up the claim.
Obama, vastly more animated than in his first debate, accused Romney of misleading voters about his record on China, the U.S. auto industry and U.S. energy production.
"What Governor Romney said just isn't true," Obama said in one of several exchanges in which he practically called his opponent a liar. He was referring to Romney's description of the 2009 bailout of General Motors and Chrysler, when Romney opposed the heavy infusion of federal funds to help the companies survive bankruptcy.
Obama used similar language to describe Romney's assessment of U.S. oil production, and the president's immigration policies.
Romney took his own whacks at the president's trustworthiness. But Romney was at his best when he kept things simple and forward-looking. He said Obama's four-year record is the best indicator of what a second term would bring.
"If you were to elect President Obama, you know what you're going to get," Romney said. "You're going to get a repeat of the last four years. We just can't afford four more years like the last four years."
"We don't have to settle for what we're going through," Romney said, urging Americans to fire a president they generally like, according to polls. "We don't have to settle for unemployment at a chronically high level. We don't have to settle for 47 million people on food stamps."
Given that unemployment just recently fell below 8 percent for the first time since he took office, Obama cannot make rosy promises without looking foolish or insincere. He acknowledged that Americans are struggling. But he urged them to stick with policies showing slow but steady improvement.
"We've created 5 million jobs, and gone from 800,000 jobs a month being lost, and we are making progress," the president said. "We saved an auto industry that was on the brink of collapse."
Obama was most animated when claiming that Romney is trying to sell voters a bill of goods. He said Romney outlines feel-good plans for lower tax rates and higher military spending that would cost $8 trillion over 10 years. The only possible ways to absorb such costs, Obama said, would involve sharply increasing the deficit or finding new ways to tax the middle class -- or both.
Slyly complimenting his opponent as "a very successful investor," Obama said that if someone approached Romney "with a plan that said, 'Here, I want to spend 7 or 8 trillion dollars, 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 indignantly said he can fulfill his promises. He would limit tax deductions for the wealthy, among other things, he said.
But independent analysts say Romney's plan would have to embrace more painful tax hikes or painful spending cuts to make the numbers work. Rather than offer such details, Romney repeatedly asked Americans to trust his skills and intentions.
"As president, I'll get America working again," he said. "I will get us on track to a balanced budget. The president hasn't."
Romney hit the "trust me" theme time and again.
"I was someone who ran businesses for 25 years, and balanced the budget," he said. "I ran the Olympics and balanced the budget."
Don't believe it, Obama kept saying. Look at details of Romney's past, not his vague summaries, he said.
"When he talks about getting tough on China, keep in mind that Governor Romney invested in companies that were pioneers of outsourcing to China," the president said. He was alluding to Romney's time as head of Bain Capital, a private equity firm.
Tuesday's debate brought huge relief to Democrats despondent over Obama's flat performance in the Oct. 3 forum.
"Whatever bounce Romney got from the first debate was stopped in its tracks," said Democratic strategist Doug Hattaway. "President Obama relentlessly drove the narrative that Romney can't be trusted, and put him on the defense much of the time."
Republicans said Romney's performance was far from shabby, but not quite as sharp as the president's.
"Obama was SO much better that he has to get the win," GOP consultant Rich Galen said in an email. "He was well-prepped to have at least one fact about Romney (true or not) that he could use in every question. I thought Romney looked as strong as he did in the first one, but because Obama was so much better, it may not look that way."
The two men have one more debate, on foreign policy, next Monday.
Between now and Nov. 6, the economy is unlikely to make a dramatic move one way or another. Voters have lots of facts, figures, disappointments and hopes lying before them. In the end, they'll have to decide whom they trust.
Charles Babington covers national politics for The Associated Press. Follow him on Twitter: https://twitter.com/cbabington