There is a current within the national political debate regarding the definition of the American State, both as it "should be regarded" from within and from without. However, at the end of the day, each side in this debate ends up saying something quite similar: America is a nation devoted to democratic principles and to ideas of equality and equal opportunity.
The real debate then concerns how these ideas are best defined.
Part of the ongoing debate over the American identity is America’s role in the rest of the world. People do not necessarily agree on whether or not we should be spreading democracy and helping other countries become democracies. Some people believe we should be role models for the world and help the rest of the world become like us, and others believe it is none of our business and we should let other countries be what they want to be.
Are you asking why people disagree about what the American identity is in this century? If so, it could be partly because of the changing ethnic makeup of the country. When we have been a majority-white country for our entire history, can we still be America if our majority is non-white and we have heavy doses of "foreign" cultures mixed into ours? That's one way to understand this, at least.