Mitt Romney finally found his voice Wednesday night.

After many months of awkward moments and shifting campaign messages, he forcefully and confidently stood alongside President Obama and offered an alternative economic vision to what he called Obama’s “trickle-down government approach.”

The two contenders seemed to swap roles Wednesday. Obama was the one who struggled for his footing, scowling on the split screens of millions of television viewers across the nation and often looking like a man who wished he were elsewhere.

Romney came to the debate at the University of Denver with a heavy set of goals, chief of which was to regain ground on the economy. That issue is uppermost among voter concerns and the one that Romney believes provides his greatest advantage.

Romney pressed his case against Obama’s stewardship of a disappointingly weak recovery. He sought to sharpen his own proposals and to soften the perception among voters that he favors the interests of the wealthy over those who are struggling.

“The people who are having the hard time right now are middle-income Americans. Under the president’s policies, middle-income Americans have been buried,” Romney said, echoing a damaging phrase that Vice President Biden used the day before to describe the status of average Americans over the past four years.

Obama, meanwhile, did not make many of the arguments that he and his campaign have used most effectively against Romney. He did not recount the former governor’s career in private equity, during which Romney laid off workers, or the secretly taped video in which the Republican nominee told wealthy donors that the 47 percent of Americans who do not pay federal income taxes are dependent on government and see themselves as victims.

The president also left many of Romney’s claims unchallenged. Romney asserted eight times that Obama plans to cut $716 billion from Medicare without noting that the Republican vice presidential nominee, Rep. Paul Ryan (Wis.), shepherded a budget through the House that would do the same thing.

In talking about the economy, which was the primary focus of the debate, Romney delivered none of the “zingers” that his team had boasted they were preparing. Each candidate instead dug into the details of his proposals and sharply criticized his opponent’s.

And in some areas, they ceded ground to the other, primarily to stress their differences.

Obama said he agreed with Romney that “our corporate tax rate is too high, so I want to lower it, particularly for manufacturing, taking it down to 25 percent. But I also want to close those loopholes that are giving incentives for companies that are shipping jobs overseas. I want to provide tax breaks for companies that are investing here in the United States.”

And Romney insisted that he does not want to reduce the share of taxes paid by the wealthy.

“High-income people are doing just fine in this economy,” he said. “They’ll do fine whether you’re president or I am.”

Romney also tried to draw a clearer link between his tax proposal, which heavily benefits the wealthy, and the economic benefit he insists it would provide for everyone else.

“The problem with raising taxes is that it slows down the rate of growth. And you could never quite get the job done,” he said. “I want to lower spending and encourage economic growth at the same time.”

The closest Romney came to matching his reputation as an unsentimental, bottom-line-driven executive was when he discussed the budget cuts he would make. The one he singled out was ending the government subsidy for the Public Broadcasting System, which airs the iconic children’s program “Sesame Street.”

“I love Big Bird,” Romney said. “But I’m not going to keep on spending money on things to borrow money from China to pay for.”

The central premise of the Republican nominee’s campaign has been that voters, disillusioned with Obama’s performance in reviving economic growth, would turn to Romney, who promotes the expertise and experience he gained in the corporate world.

But with less than five weeks to go before Election Day, Romney has been struggling to make a convincing case for himself on that score — and is running about even with Obama on who would better handle the economy.

Where Romney held a seven-point edge over the president on that question among registered voters in an August Washington Post-ABC News poll, the latest survey shows them tied, with 47 percent saying Romney would do a better job and the same proportion opting for Obama.

Meanwhile, the president continues to hold a double-digit advantage when voters are asked which of the two candidates better understands the economic problems people in this country are having. In the most recent poll, 52 percent said it was Obama, while only 39 percent named Romney.

The first debate, which history suggests will draw the biggest audience, amounted to Romney’s best opportunity to change a political dynamic that has been moving against him.

As a result, he was getting an avalanche of advice — some of it conflicting — from the conservative commentariat and from his allies on the sidelines: Be more aggressive, be more personable, attack Obama’s record, offer more details about his plans, stay out of the weeds and stick to big themes.

For Obama, who went into the debates with a slight lead in nearly every poll, the biggest challenge was to avoid a stumble. In past debates, his worst flaws were ones of style, in which he came off as arrogant and aloof, or long-winded and professorial.

Whether the debate did much to win over undecided voters or change anyone’s mind is not likely to become clear for at least a few days. In that time, news organization fact checkers will pick over the assertions that were made, pundits will award style points, and social media will amplify — and perhaps amend — the overall impressions that were left.

In this deeply polarized country, the number of people who are truly wavering in their choice is relatively small. And those who are probably were not among the tens of millions who tuned into the debate, said AFL-CIO political director Michael Podhorzer.

By and large, “they are undecided because those people are not checked into the election,” Podhorzer said. “They’re paying attention to the coverage of the debate and they’re paying attention to what their friends are saying.”

And in an era when so much of the national dialogue takes place on social media, “inevitably some moments will live on in YouTube,” he added.