No. Not greed. It won't be the downfall of the American Empire. Stagnation will be. What matters for the survivability of an empire is not whether it has problems. All countries run into problems from time to time. What matters is whether it can deal with them, and adapt if necessary.
The recent debacle of the debt ceiling (manufactured) crisis, and the attempted healthcare reform two years before it, quite strongly indicate that it cannot. Both were opportunities to fix something inherently dysfunctional. In both cases, deliberate obstructionism by dogmatic, inflexible, uncompromising Republicans led to a solution that may have made some cosmetic changes, but mostly just led to more money being thrown into the meatgrinder. The reason why they could do it? The power of stupid, of stupid people believing in simple explanations of complex realities, and in simple solutions to complex problems. People for whom American exceptionalism is axiomatic, who delude themselves to believe they are living in a shining city on a hill, shooting those who disagree, the very people who are trying to save it from sinking into the mud.