(CBS News) CHARLOTTE, N.C. -- President Obama formally accepted the Democratic party's presidential nomination on Thursday night, calling the 2012 election "the clearest choice of any time in a generation."

"On every issue, the choice you face won't be just between two candidates or two parties," the president said on the final night of the Democratic National Convention, in front of a crowd of about 20,000 at the Time Warner Cable Arena. "It will be a choice between two different paths for America. A choice between two fundamentally different visions for the future."

The president appealed to his supporters to keep up faith they showed during the 2008 campaign, even as his promises of "hope" and "change" are tested.

"Know this, America: Our problems can be solved. Our challenges can be met," he said. "The path we offer may be harder, but it leads to a better place. And I'm asking you to choose that future. I'm asking you to rally around a set of goals for your country - goals in manufacturing, energy, education, national security, and the deficit; a real, achievable plan that will lead to new jobs, more opportunity, and rebuild this economy on a stronger foundation."

Mr. Obama noted that in the next four years, Washington would be forced to make critical decisions on all of those issues. He warned that his Republican rival Mitt Romney would revive stale policies that failed in the past and will surely fail again. And while acknowledging that voters may be second-guessing their faith in his leadership, Mr. Obama said his own policies have shown a clear path to progress.

The president made some of the sharpest contrasts between his policies and Romney's proposals on the subject of foreign policy.

"Four years ago, I promised to end the war in Iraq. We did," he said. "I promised to refocus on the terrorists who actually attacked us on 9/11. We have. We've blunted the Taliban's momentum in Afghanistan, and in 2014, our longest war will be over. A new tower rises above the New York skyline, al Qaeda is on the path to defeat, and Osama bin Laden is dead."

The president listed off the challenges that remain on the world stage, including terrorist plots, the European debt crisis, Iran's nuclear ambitions and revolution in the Middle East. Then with a bit of a sarcastic tone, he alluded to the foreign policy gaffes Romney made this year.

"My opponent and his running mate are new to foreign policy, but from all that we've seen and heard, they want to take us back to an era of blustering and blundering that cost America so dearly," he said. "After all, you don't call Russia our number one enemy - and not al Qaeda - unless you're still stuck in a Cold War mind warp. You might not be ready for diplomacy with Beijing if you can't visit the Olympics without insulting our closest ally."