DENVER — With the presidency hanging in the balance, President Barack Obama and Republican challenger Mitt Romney clashed sharply Wednesday in their first debate, trying to convince voters they’re uniquely qualified to lead the country to full recovery from the worst economic downturn since the 1930s.

The economy and domestic issues were the focus of the 90-minute showdown between the presidential candidates, the first of three nationally televised face-offs with an audience expected to total in the tens of millions. They met at the University of Denver at a time when the country remained closely divided between the two and millions of Americans are looking for the best path to restore jobs and paychecks. Jim Lehrer of PBS moderated the debate.

“We’ve begun to fight our way back,” Obama said at the outset, arguing that his policies are turning the economy around. “We’ve still got a lot of work to do.”

Romney countered by noting his encounters with people who have approached him in recent days asking for help finding work for themselves or their families. “We can help, but it’s going to take a different path,” Romney said. “The path that we’re on has been unsuccessful. Trickle down government will not work.”

The debate opened with a personal moment, Obama noting it was his 20th wedding anniversary and he’s the “luckiest man on Earth.” Then he launched into a recitation of what he called progress on the economy.

“Governor Romney has a perspective that says if we cut taxes skewed toward the wealthy and cut regulations, we’ll be better off. I have a different view,” he said. He would stress education and training, and reduce the federal deficit in a “balanced way.” He called for a “new economic patriotism” that says “America does best when the middle class does best.”

Romney joked that the debate was clearly the most romantic place Obama could be on his anniversary. Then he got serious.

He said Obama’s policies haven’t worked. Romney described his five-part plan, including a path to a balanced federal budget, getting tougher with China and being friendlier to small business.

“I know what it takes to get small business growing again,” he said. Obama, Romney charged, has a view that emphasizes taxing more, regulating more and growing government. “I’ll restore the vitality that gets American working again,” Romney said.

Romney called Obama’s approach “trickle-down government.” Obama, asked to respond, suggested corporate tax rates should go down, but he also wants to close loopholes for companies shipping jobs overseas. On energy, Obama said, he and Romney agree domestic energy production needs to be boosted. But Obama also wants to promote “energy sources of the future,” like wind and biofuels.

Romney said Obama had exaggerated the tax cut he proposes. “The people who are having a hard time right now are middle-income Americans,” Romney said, adding middle-income people are being “buried,” a phrase used by Vice President Joe Biden this week. Romney was not precise about how Obama was exaggerating.

“I’m not looking to cut massive taxes,” he said, and pledged “no tax cut that adds to the deficit,” though he would not provide specifics. Romney would retain Bush-era tax cuts and slice income tax rates 20 percent across the board. Obama would retain the Bush rates only for families earning less than $250,000 and individuals making less than $200,000.

The candidates will debate again Oct. 16 in Hempstead, N.Y., and on Oct. 22 in Boca Raton, Fla. Biden will debate Republican nominee Rep. Paul Ryan of Wisconsin on Oct. 11 in Danville, Ky.

Heading into the debate, the race boiled down to a series of charges and countercharges backed by waves of negative TV ads seen in swing states (only about 10 states are really seen as up for grabs). Romney argues that he has the business skills to help create jobs and that Obama’s policies of more government spending and regulation have slowed the recovery. Obama counters that his fixes are working, albeit slowly, and that Romney’s tax cuts would help the wealthy and make deficits worse.

Voting already has begun in 35 states.

High on the list for Wednesday: disagreements over taxes, government spending, the new government health care law and immigration.

Obama has an edge over Romney in most national and swing state polls. But Romney holds the edge on the economy. A Gallup poll released Wednesday found that voters think Romney would better handle the economy by 49 percent to 45 percent. The survey also showed slightly more voters think the economy will be better if Romney wins.

Part of the voters’ judgment is likely to involve their perceptions of how things are going, and economic indicators are mixed. Unemployment has topped 8 percent since February 2009, the month after Obama took office, an unusually long stretch for such a high rate. But the president can argue that unemployment has slowly dropped since its 10 percent peak two years ago.

The economy grew at a sluggish 1.3 percent annual rate in the second quarter of this year, hardly considered a healthy pace. But it did grow, and it has been expanding since the Great Recession of 2007-09 ended more than three years ago.

Consumer confidence, a key barometer of public mood, jumped last month, but even that spike only brought it back to its February level, according to data compiled by the Conference Board, a New York-based research group.

And household income continues to lag. A study by Sentier Research found that in the three years ending in June, inflation-adjusted median household income tumbled 4.8 percent, even worse than the 2.7 percent drop during the recession itself.

To Romney, those numbers are strong evidence that the economy needs help, and that a bloated government and its spiraling debt has hurt it badly. Leading up to the debate, he argued that there’s been a huge redistribution of wealth from the wealthy to lower income people, and his camp has been citing a 1998 recording of Obama backing the idea.

A Wall Street Journal study of census figures found that 49.4 percent of people lived in a household where people got some government help, well above the 30 percent of the 1980s.

“We can’t afford four more years of Obama’s failed policies. This is not what a real recovery looks like,” said Ed Gillespie, a senior adviser to Romney.

Romney also attacks the 2010 federal health care law that Obama views as a signature achievement of his presidency. The law requires nearly everyone to obtain coverage by 2014. Romney vows to fight for repeal.

Obama vigorously defends his policies. He’s countered that without government stimulus, the economy would be in even worse shape, as he offers “a genuine sense of what we’ve been through over the last four years,” Obama campaign adviser Robert Gibbs said.

The president, he said, planned to discuss “the progress we’ve made going forward and then, most importantly, what we have to do over the next four years to continue strengthening our economy, building our economy from the middle out, putting more people back to work, and strengthening our education system, a whole host of things.”