(AP) - 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 that blended resolve about the challenges ahead with stinging criticism of Republican rival Mitt Romney's proposals to repair the economy.

He acknowledged "my own failings" as he asked for a second term, four years after taking office as the nation's first black president.

"Four more years," delegates chanted over and over as the 51-year-old Obama stepped to the podium, noticeably grayer than four years ago when he was a history-making candidate for the White House.

The president'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 Republican rival Romney. The contest is ever tighter for the White House in a dreary season of economic struggle for millions.

Vice President Joe 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."

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.

Former President Clinton wraps up second day of DNCFirst night of the DNC closes with first lady address