His re-election in doubt, President Barack Obama accepted his party's presidential nomination Thursday night, acknowledging slow progress in solving the nation's economic woes but declaring, "Our problems can be solved, our challenges can be met."

"The path we offer may be harder, but it leads to a better place," he said.

"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.

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, Jill. Strains of "Only in America" filled the hall as confetti filled the air.

His speech was the final act of his national convention, and the opening salvo of a two-month drive toward Election Day in his race against Republican rival Mitt Romney. The contest is close for the White House in a dreary season of economic struggle for millions.

With unemployment at 8.3 percent, Obama 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 the Great Depression 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."

Romney answered the speech by issuing a statement saying Obama hadn't kept his promises: “Tonight President Obama laid out the choice in this election, making the case for more of the same policies that haven't worked for the past four years."

The convention's final night also included a nomination acceptance speech from Biden, whose appeal to blue collar voters rivals or even exceeds Obama's own.

Biden told the convention 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."

With Obama in the hall listening, Biden jabbed at the president's challenger, as well.

"I found it fascinating last week — when Governor Romney said that as president he'd take a jobs tour,” he said. “Well with all his support for outsourcing — it's going to have to be a foreign trip."

Mrs. Obama, popular with the public, introduced her husband, two nights after she delivered her own speech in the convention's opening session.

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.

The hall erupted in tumultuous cheers when former Arizona Rep. Gabrielle Giffords, grievously wounded in a 2011 assassination attempt, walked slowly onto the stage to lead the Pledge of Allegiance. The cheers grew louder when she blew kisses at the crowd.

Delegates also cheered when 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, approved by the current commander in chief.

"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.

Actress Eva Longoria was on the program, as well. "No empty chairs," she said, a reference to actor Clint Eastwood's mocking reference to Obama at Romney's Republican National Convention last week in Florida.

Obama said he would set a goal of creating 1 million new manufacturing jobs by the end of 2016 and push for more aggressive steps to reduce American dependence on foreign oil.

He also called for curtailing the growth of college costs by half over the next 10 years. According to the Department of Education, the price of undergraduate tuition and room and board at public institutions rose by 42 percent in the decade that ended in 2010; the increase at private not-for-profit institutions was 31 percent.

Still, he said, "The truth is it will take more than a few years for us to solve challenges that have built up over decades."

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.

Convention planners shoehorned a few more seats into the Time Warner Cable Arena for Obama's remarks, pushing capacity to about 15,000. Even so, the decision to scrap plans to hold the night's session in a 74,000-seat football stadium meant a far smaller crowd than the president's campaign hoped would hear him speak and present an enthusiastic show of support on television.

Officials blamed the switch on weather concerns, and there was heavy rain at mid-afternoon. Perhaps typical of delegates and their feelings, Grifynn Clay of Snohomish, Wash., said, "I would've enjoyed the stadium, but if it was pouring I would not want to be in there for the six hours of speeches."

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.

"I refuse to ask middle class families to give up their deductions for owning a home or raising their kids just to pay for another millionaire’s tax cut," he said. "I refuse to ask students to pay more for college; or kick children out of Head Start programs, or eliminate health insurance for millions of Americans who are poor, elderly, or disabled — all so those with the most can pay less."

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.

He also said he had no plans to watch Obama on television.

"If the president is going to report on the promises he made and how he has performed in those promises, I'd love to watch it," Romney said. "But if it's another series of new promises that he's not going to keep, I have no interest in seeing him because I saw the promises last time."

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.

"We've got 17 angry, old, white men who are pouring in millions of dollars, carpet bombing every candidate in sight," said Sen. Dick Durbin of Illinois, referring to wealthy Republicans who have written checks for a million dollars or more to Americans for Prosperity and Restore Our Future.

Officials disclosed that former President who made a forceful convention speech advocating Obama's re-election on Wednesday night, would campaign aggressively for the Democratic ticket this fall. His first appearance is set for Florida next week.

On Obama's conference call to supporters who were cut out of seeing Thursday night's session, Obama exhorted them to continue their work on voter registration and other pre-election activity.

He said North Carolina is "Exhibit A of the unbelievable work that's being done at the grassroots level. You guys are blowing it up when it comes to registering voters."

Official figures show about 30,000 Democrats have been registered to vote in the state since 2008, but some party leaders said recent canvassing had pushed the actual figure far higher.

On the call, the president commiserated with those who would no longer be able to see him speak.

"The problem was a safety issue. I could not ask you, all volunteers, law enforcement, first responders to subject themselves to the risk of severe thunderstorms," he said.

A few hours later, the skies opened up with a torrential downpour.

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.