Romney said if elected he would seek to eliminate Obama's healthcare reform package. "It has killed jobs," the former Massachusetts governor said, adding he would rather see individual states craft their own healthcare plans as he did in Massachusetts.
Obama said his healthcare reform has helped provide coverage for millions of uninsured people, and later said Romney would have a hard time getting Democrats in Congress to go along with wiping out "Obamacare," a term the president embraced.
The two parted ways on the role of the federal government, with Obama saying it has "the capacity to open opportunities" for people.
"Also, there are some things we do better together," Obama said.
Romney said Americans "care for those with difficulties. But we also believe in the right of individuals to pursue their dreams."
Romney said Obama promotes "trickle-down government, which has the government thinking it can do a better job than people in pursuing their dreams."
The result, he said, is an increase in the number of people on food stamps from 30 million to 47 million and half of this year's college graduates unable to find work.
On education, Obama said Romney's plan, while not very detailed, would result in a 20 percent cut in the federal education budget. Investing in education, Obama said, "is how we're going to grow this economy over the long run."
But Romney said he's not going to cut education funding and faulted Obama for putting $90 billion in so-called green industries. "That would have hired 1 million teachers," Romney said. "I propose we grade schools."
"The right course for America's government is not to become the economic player, picking winners and losers," Romney said.
"It's time," he said, "for a new path."
Asked what they would do to create jobs in the next four years, Obama said he would put money into education and training, developing new sources of domestic energy and changing the tax code.
He said he would take "some of the money we're saving as we wind down two wars and reinvest in America." Obama said it would be wrong to "double down on the top-down policies" that led to the Great Recession and called for "economic patriotism" from the nation's wealthiest to help move the country forward.
Romney laid out his five-point plan to increase domestic energy, open up trade, improve worker skills, balance the budget and "champion small businesses." He said business start-ups are at a 30-year low and blamed "trickle-down government."
Romney said he wants to reduce income tax rates and tighten credits and deductions. Obama contended Romney wants to implement $5 trillion in tax cuts and add $2 trillion in military spending, and that even if all loopholes were eliminated for the wealthy, it wouldn't add up to $7 trillion so the burden would fall on the middle class.
Romney denied he would cut taxes $5 trillion.
"I will not reduce the taxes paid by high-income Americans," Romney said. "I will not raise taxes on middle-class families. I will lower them."
Obama said he doesn't buy it.
"For 18 months he's been running on this tax plan. Now, five weeks before the election, his big, bold idea is 'never mind," Obama said. "It's not possible to come up with enough deductions [to eliminate]. It's math. It's arithmetic."
Romney blasted Obama for wanting to raise taxes on the top 3 percent, saying it would cost 700,000 jobs.
On the deficit, Romney said Obama "would prefer raising taxes."
"The problem is, that slows down the rate of growth," Romney said. "I want to slow spending and improve the rate of growth."
When it comes to spending, Romney said he wants to make government more efficient, and his measuring stick would be a program must be "important enough to borrow money from China."
"The president said he would cut the deficit in half. Unfortunately, he doubled it," Romney said.
Obama noted he has cut $1 trillion in discretionary domestic spending and has put forth a plan to cut $4 trillion more.
He said the "major difference" between him and Romney is that he wants a balanced approach and Romney "has ruled out revenue."
"If we're asking for no revenue, you're going to have to cut a whole bunch of stuff," Obama said. "That will be a severe hardship for people, but more importantly, it would not help us to grow."
The second debate, Oct. 16, at a 5,000-seat sports and exhibition complex at Hofstra University near New York City, is to be a "town meeting" format moderated by CNN "State of the Union" host Candy Crowley.
The third debate, Oct. 22, at a 750-seat performing arts center at Lynn University in Boca Raton, Fla., is expected to focus on foreign policy and be moderated by CBS News "Face the Nation" host Bob Schieffer.
Notable deaths of 2014 [PHOTOS]