Oh man, this should be fun to debate. I would put my life, my car, my house, everything on the UNDER 300 years before the US falls. Honestly, I think another country or group of countries pulls even with us within the next 50 years.
The thing with the United States is that most of the world has already turned on them and it shouldn't be long before they fall. What people also don't realize is that one of our main power bases is evaporating right in front of our eyes. Criticize him all you want, but Chavez is using his oil revenues smarter than any of the Middle East countries ever will. Chavez is using that oil money to support leftist movements around Latin America. This hurts the US because for over 200 years we have exploited Latin America for our economic gain whenever possible. Look at NAFTA, sure we lost some jobs but they were crap jobs that few Americans really wanted. Yet from Mexico we got to create a bunch of white collar jobs in Mexico and America from the maquiladoras and other industries. We also get food cheaper from them while keeping the tariffs up in agriculture where they have an advantage against us. Also, we are now able to sell the new corn and potato seeds to the indigenous farmers and make a KILLING.
However, Chavez is trying to put a stop to this and so far he has met with a good amount of success. Rather than just relying on the US, in this era of globalization Chavez has diversified his economy and has happily invited over Russian, Chinese, and Indian investors. This diversification allows Venezuela not to be at the beck and call of the United States. I will admit, I was skeptical at first, and I still expect to hear Chavez have a "heart attack" in the near future followed by a conspicuous death of Morales in Bolivia a few months later as well. However, his reforms have had some success. He is trying to create in Latin America a system somewhat similar to the EU. If he is successful in this, the US could be in a LOT of trouble economically. This is because the US's most reliable partners are Mexico, Central America, and Canada. Canada and Mexico are the only ones with a halfway decent world economy of all of these.
The US also has to worry about a terror threat that no other empire has had to worry about. Terrorism will surely strike again on US soil. The US has way too many problems to last forover 300 years.
In regards for who will be the next empire, I would not go with China. A huge population yes, but there are better countries to look at. I would go with either India or the EU bloc (providing they stop the conflicting processes of integration and separation)