DENVER – With the presidency hanging in the balance, President 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 two men sparred from the opening minutes over their competing visions of government and whether it should help lead the way to a better economy or get out of the way. Each also repeatedly accused the other of promoting damaging policies on such issues as taxes, spending, health care and business regulation that made or would make things worse, not better.

“We’ve begun to fight our way back,” Obama said, arguing that he has helped turn around the economy but needs four more years to finish the job. “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.”

They met at the University of Denver, standing on a stage with the texts of the Constitution and the Declaration of Independence over their shoulders at a time when the country remains closely divided between the two and millions of Americans are looking for the best path to restore jobs and paychecks.

Romney tended to be more fiery and aggressive, offering a starkly different menu of changes in how Americans are taxed and seniors get health care, a performance that could help him get his struggling campaign back on track. Obama tried to paint Romney as extreme and irresponsible, but he appeared defensive at times, pursing his lips and looking down rather than at Romney.

The two, who have met a handful of times, were cordial with each other, addressing each as “Mr. President” and “Governor” before they launched their fact-filled attacks. They even laughed about sharing a stage on the Obamas’ 20th wedding anniversary.

But they were resolute in their arguments, each aggressively defending his proposals or criticizing the other even when moderator Jim Lehrer tried to stop them after they exceeded time limits.

Romney said he had plans to fix the economy, overhaul the tax code, repeal Obama’s health care plan and replace it with a better alternative, remake Medicare, pass a substitute for the legislation designed to prevent another financial crash, and reduce deficits — but he provided no new specifics despite Obama’s prodding.

Said Obama: “At some point the American people have to ask themselves: Is the reason Governor Romney is keeping all these plans secret, is it because they’re going to be too good? Because middle-class families benefit too much? No.”

Romney argued that Obama has presided over a weak recovery that has “crushed” the middle class.

“Under the president’s policies, middle-income Americans have been buried,” Romney said. “They’re just being crushed. Middle-income Americans have seen their income come down by $4,300. This is a tax in and of itself. I’ll call it the economy tax. It’s been crushing. At the same time, gasoline prices have doubled under the president. Electric rates are up. Food prices are up. Health care costs have gone up by $2,500 a family. Middle-income families are being crushed.”

He tore into Obama’s signature domestic achievement, the 2010 health care law, calling it a misplaced priority at a time that Americans yearned mostly for jobs.

“I just don’t know how the president could have come into office, facing 23 million people out of work, rising unemployment, an economic crisis at the kitchen table, and spend his energy and passion for two years fighting for Obamacare instead of fighting for jobs for the American people,” he said.

The president accused Romney of wanting to give tax breaks to the wealthy instead of helping the middle class, which he said would create jobs and boost 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.

Obama said he supports a “balanced approach” of tax cuts and increased spending. He said he would stress education and training, calling for a “new economic patriotism” that says “America does best when the middle class does best.”

Romney repeatedly said descriptions of his tax plan were not true, and he accused the president of distorting his proposals. He wants to extend George W. Bush-era tax cuts that lowered the tax rate paid by Americans at all income levels and enact additional cuts.

“Virtually everything he said about my tax plan is inaccurate. My plan is not like anything that has been tried before,” Romney said. “Going forward with the status quo is not going to cut it anymore.”

Obama suggested that corporate tax rates should go down, but he also wants to close loopholes for companies shipping jobs overseas. Taxes and the deficit dominated the first part of the 90-minute showdown between the two presidential candidates, the first of three nationally televised face-offs with an audience expected to total in the tens of millions. But also on the list was health care, the role of government and Social Security and Medicare.

Both Obama and Romney insisted they know how important it is to cut the nation’s debt. Obama said he has tried to cut the debt that has ballooned because of the cost of two wars, tax cuts and government programs that were not paid for. He insisted that he worked with Democrats and Republicans to cut a trillion dollars and is working to convince a divided Congress to cut $4 trillion from the projected deficit.

“It’s on a website. You can look at all the numbers, what cuts we make and what revenue we raise,” he said.

But Romney said Obama had time to reduce the deficit and failed. They also clashed on health care, and few issues divide the candidates and their parties more than that issue. The 2010 federal health care law championed by Obama would require nearly everyone to get coverage by 2014. Romney sees the plan as a dangerous government takeover.

They also differ on how seniors should obtain care. Obama wants to retain traditional Medicare, which faces a severe financial crisis. He would save $716 billion from anticipated spending in the future; part of that money would be saved by having an independent commission recommend ways to cut costs.

Romney fired away at that notion and insisted his plan, which would provide federal help for seniors so they could choose Medicare or a private plan, was far more efficient.

“I know my own view is I’d rather have a private plan. I’d just as soon not have the government telling me what kind of health care I get. I’d rather be able to have an insurance company. If I don’t like them, I can get rid of them and find a different insurance company. But people make their own choice,” he said.

No, Obama countered. Private plans will insure the healthiest seniors, leaving Medicare to take the most ailing. “And when you move to a voucher system, you are putting seniors at the mercy of those insurance companies. And over time, if traditional Medicare has decayed or fallen apart, then they’re stuck,” the president said.

Obama recalled how Romney signed into law the Massachusetts health care plan widely seen as a model for the federal program.

“There’s a reason why Governor Romney set up the plan that he did in Massachusetts. It wasn’t a government takeover of health care. It was the largest expansion of private insurance,” Obama said.

Romney defended his plan, noting that it raised no taxes. But, he added, “The federal government taking over health care for the entire nation and whisking aside the 10th Amendment, which gives states the rights for these kinds of things, is not the course for America to have a stronger, more vibrant economy But what it does say is that insurers, you’ve got to take everybody.”

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