Third parties generally emerge when some sort of major change makes the previous party system impossible to maintain. For example, it was the splits between the North and South leading up to the Civil War that led to the death of the Whig Party and the eventual creation of the Republican Party. So the question then becomes whether there is such a major change taking place today.
One can certainly argue that there is. The rise of the Tea Party and of anger about government spending and taxes (while at the same time people demand that their Medicare and Social Security not be touched) is putting a great deal of stress on the political system. Neither party seems at this point to be able to come up with a way of satisfying voters that seems likely to be workable and long-lasting. In such an environment, with the US population aging, globalization increasing, and questions arising about the role of government, it could be that the time is ripe for a third party to arise.