But Rice said Americans must solve several challenges of its own to show the world that democracy still works, and is something they should follow.
"What we see in Washington, D.C., these days is pretty tough to watch," she said as Hatch skipped his own women's conference while Congress debates the federal-government shutdown. She said politicians not being able to work with those who don't share their beliefs is a growing problem.
"Yes, you have to stand on principle," she said, "but you also have to know the difference between principle and public policy."
She said it is easy in today's world to receive news and blogs only from people who share the same views. If you find yourself with company where everyone "says amen to everything you say, you need to find new company," Rice said. Sticking only with like-minded people will cause you either to lose your ability to defend your views or the ability to see when you are wrong.
She added that if people never encounter others with whom they disagree, they "start to think of them as stupid or venal because you don't have the chance to exchange views."
One problem America needs to solve is immigration reform, Rice said. The country is great in part because of the innovation and risk-taking it allows, she said, and immigration brings new ideas to continually rejuvenate that process.
"That's why immigration reform is important," she said. "We need to find those people who want to come and be part of that creativity."
She called declining education in public schools is "maybe the single biggest national security threat." Rice said quality education is the key to good employment, and too many are not receiving it. That could condemn them to unemployment, living on the dole and a growing sense of aggrievement and entitlement and a drain on society.
Rice said the world needs an example of hope as it works through changes and shock caused by the 9/11 bombings, the recession and recent Middle East unrest as citizens there try to seize control of their governments.
"The seizing of rights is not democracy," Rice said, but Americans shouldn't be too harsh in their judgment. "We were once those people," noting the Founding Fathers seized their rights but took years to develop institutions to protect them and allow people to expect that they peacefully can bring change within the system.
America "will lead the world to a better place," she said, if "we find the will."