CHARLOTTE, N.C. — His re-election in doubt, President Barack Obama conceded only halting progress Thursday night toward fixing the nation’s stubborn economic woes but vowed in a Democratic National Convention finale, “Our problems can be solved, our challenges can be met.”

“Yes, our path is harder – but it leads to a better place,” he declared in a prime-time speech to convention delegates and the nation, blending resolve about rescuing the nation from near economic catastrophe with stinging criticism of Republican rival Mitt Romney’s own proposals.

Widely viewed as reserved, even aloof, Obama acknowledged “my own failings” as he asked for a second term, four years after taking office as the nation’s first black president.

Citing progress toward recovery, he said, “After a decade that was defined by what we bought and borrowed, we’re getting back to basics and doing what America has always done best: We’re making things again.”

“Four more years,” delegates chanted over and over as the 51-year-old Obama stepped to the podium, noticeably grayer than he was as a history-making candidate for the White House in 2008.

First Lady Michelle Obama and the couple’s daughters, Malia and Sasha, joined the president on stage in the moments after the speech, followed by other family members and Vice President Joe Biden and his wife. Strains of “Only in America” filled the hall as confetti filled the air.

Obama’s speech was the final act of a pair of highly scripted national political conventions in as many weeks, and the opening salvo of a two-month drive toward Election Day that pits Obama against Romney, the former governor of Massachusetts.

Not only economic proposals will settle a tight contest for the White House in a dreary season of economic struggle for millions, but also campaign cash.

There, Romney holds an advantage for sure. His campaign has purchased about $4.5 million in television advertising for the next several days, according to officials who track such spending. Obama, by contrast, emailed a fundraising appeal to supporters two hours before his convention speech.

Biden preceded Obama at the convention podium and proclaimed, “America has turned the corner” after experiencing the worst economic crisis since the Great Depression.

Obama didn’t go that far in his own remarks, but he said firmly, “We are not going back, we are moving forward, America.”

With unemployment at 8.3 percent, the president said the task of recovering from the economic disaster of 2008 is exceeded in American history only by the challenge Franklin Delano Roosevelt faced when he took office in 1933.

“It will require common effort, shared responsibility and the kind of bold persistent experimentation” that FDR employed, Obama said.

In an appeal to independent voters who might be considering a vote for Romney, he added that those who carry on Roosevelt’s legacy “should remember that not every problem can be remedied with another government program or dictate from Washington.

He said, “The truth is, it will take more than a few years for us to solve challenges that have built up over the decades.”

The Romney campaign was dismissive as Democrats completed their convention.

“Americans will hold President Obama accountable for his record – they know they’re not better off and that it’s time to change direction,” Matt Rhoades, the challenger’s campaign manager, said in a statement.

In the run-up to Obama’s speech, delegates erupted in tumultuous cheers when former Arizona Rep. Gabrielle Giffords, grievously wounded in a 2011 assassination attempt, walked onstage to lead the Pledge of Allegiance. The hall grew louder when she blew kisses to the crowd.

And louder still when huge video screens inside the hall showed the face of Osama bin Laden, the terrorist mastermind killed in a daring raid on his Pakistani hideout by U.S. special operations forces on a mission approved by the current commander in chief.

The hall was filled to capacity long before Obama stepped to the podium, and officials shut off the entrances because of a fear of overcrowding for a speech that the campaign had originally slated for the 74,000-seat football stadium nearby. Aides said weather concerns prompted the move to the convention arena, capacity 15,000 or so.

Obama’s campaign said the president would ask the country to rally around a “real achievable plan that will create jobs, expand opportunity and ensure an economy built to last.”

He added, “The truth is it will take more than a few years for us to solve challenges that have built up over a decade.”

In convention parlance, both Obama and Biden were delivering acceptance speeches before delegates who nominated them for new terms in office.

But the political significance went far beyond that – the moment when the general election campaign begins in earnest even though Obama and Romney have been pointing toward a Nov. 6 showdown for months.

To the cheers of delegates, Obama retraced his steps to halt the economic slide, including the auto bailout that Romney opposed.

“After a decade of decline, this country created over a half million manufacturing jobs in the last two and a half years,” he said.

Turning to national security, he said he had promised to end the war in Iraq, and had done so.

“We’ve blunted the Taliban’s momentum in Afghanistan, and in 2014 our longest war will be over,” he said.

“A new tower rises above the New York skyline, al-Qaida is on the path to defeat and Osama bin Laden is dead,” he declared, one of the night’s repeated references to the special operations forces raid that resulted in the terrorist mastermind’s demise more than a year ago.

He lampooned Romney’s own economic proposals.

“Have a surplus? Try a tax cut. Deficit too high? Try another. Feel a cold coming on? Take two tax cuts, roll back some regulations and call us in the morning,” he said.

Mocking Romney for his overseas trip earlier this summer, Obama said, “You might not be ready for diplomacy with Beijing if you can’t visit the Olympics without insulting our closest ally.” That was a reference to a verbal gaffe the former Massachusetts governor committed while visiting London.

The hall was filled to capacity long before Obama stepped to the podium, and officials shut off the entrances because of a fear of overcrowding for a speech that the campaign had originally slated for the 74,000-seat football stadium nearby. Aides said weather concerns prompted the move to the convention arena, capacity 15,000 or so.

Obama’s campaign said the president would ask the country to rally around a “real achievable plan that will create jobs, expand opportunity and ensure an economy built to last.”

Biden told the convention in his own speech that he had watched as Obama “made one gutsy decision after another” to stop an economic free-fall after they took office in 2009.

Now, he said, “we’re on a mission to move this nation forward” from doubt and downturn to promise and prosperity. ... America has turned the corner.”

Delegates who packed into their convention hall were serenaded by singer James Taylor and rocked by R&B blues artist Mary J. Blige as they awaited Obama’s speech.

There was no end to the jabs aimed at Romney and the Republicans.

“Ask Osama bin Laden if he’s better off than four years ago,” said Massachusetts Sen. John Kerry, who lost the 2004 election in a close contest with President George W. Bush. It was a mocking answer to the Republicans’ repeated question of whether Americans are better off than when Obama took office.

The campaign focus was shifting quickly to politically sensitive monthly unemployment figures due out Friday morning and the first presidential debate on Oct. 3 in Denver. Wall Street hit a four-year high a few hours before Obama’s speech after the European Central Bank laid out a concrete plan to support the region’s struggling countries.

The economy is by far the dominant issue in the campaign, and the differences between Obama and his challenger could hardly be more pronounced.

Romney wants to extend all tax cuts that are due to expire on Dec. 31 with an additional 20 percent reduction in rates across the board, arguing that job growth would result. He also favors deep cuts in domestic programs ranging from education to parks, repeal of the health care legislation that Obama pushed through Congress and landmark changes in Medicare, the program that provides health care to seniors.

Obama wants to renew the tax cuts except on incomes higher than $250,000, saying that millionaires should contribute to an overall attack on federal deficits. He also criticizes the spending cuts Romney advocates, saying they would fall unfairly on the poor, lower-income college students and others. He argues that Republicans would “end Medicare as we know it” and saddle seniors with ever-rising costs.

After two weeks of back-to-back conventions, the impact on the race remained to be determined.

"You’re not going to see big bounces in this election,” said David Plouffe, a senior White House adviser. “For the next 61 days, it’s going to remain tight as a tick.”

Romney wrapped up several days of debate rehearsals with close aides in Vermont and is expected to resume full-time campaigning in the next day or two.

In a brief stop to talk with veterans on Thursday, he defended his decision to omit mention of the war in Afghanistan when he delivered his acceptance speech last week at the Republican National Convention. He noted he had spoken to the American Legion only one day before.

Romney’s campaign released its first new television ad since the convention season began.

It shows Clinton sharply questioning Obama’s credibility on the Iraq War in 2008, saying “Give me a break, this whole thing is the biggest fairy tale I’ve ever seen.” Obama was running against Hillary Rodham Clinton at the time for the Democratic nomination.

It will likely be a week or more before the two campaigns can fully digest post-convention polls and adjust their strategies for the fall.

Based on the volume of campaign appearances to date and the hundreds of millions of dollars spent already on television advertising, the election appears likely to be decided in a small number of battleground states. The list includes New Hampshire, Virginia, Ohio, Colorado, Nevada and Iowa, as well as Florida and North Carolina, the states where first Republicans and then Democrats held their conventions. Those states hold 100 electoral votes among them, out of 270 needed to win the White House.

Money has become an ever-present concern for the Democrats, an irony given the overwhelming advantage Obama held over John McCain in the 2008 campaign.

This time, Romney is outpacing him, and independent groups seeking the Republican’s election are pouring tens of millions of dollars into television advertising, far exceeding what Obama’s supporters can afford.

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Associated Press writers Leo Buckle, Ben Feller, Ken Thomas, Matt Michaels and Jim Kuhnhenn in Charlotte, Calvin Woodward, Jennifer Agiesta, Jack Gillum and Josh Lederman in Washington, Kasie Hunt in Vermont and Thomas Beaumont and Steve Peoples in Iowa contributed to this report