This question appears from time to time particularly in sensationalist literature and is largely drawn from Edward Gibbon's Decline and Fall of the Roman Empire. Gibbon's work was a masterpiece of the time, although it is largely discounted by most modern historians. He indicated that internal problems, not foreign invasion brought down the Empire, including something of a complete moral collapse which "contaminated the Roman soul and mind."
One cannot easily compare the United States to Rome, as the world is a different place. We have different governmental systems, different defense mechanisms, and entirely different cultures. Those who tend to compare the two typically manifest little understanding of either. Having said that, Oswald Spengler, who wrote The Decline of the West was at least partially correct in indicating that all great empires eventually enter a state of decline. Although the United States is the worlds oldest surviving democracy and probably will be for some time, it is entirely possible that its place on the world stage will eventually subside somewhat. To compare this change of status to the collapse of the Roman Empire is however a reach beyond anything but the wildest imagination.
I'm not sure that comparing the bloated nature of the Roman Empire to the U.S.'s "overstretching" is a fair comparison. There simply isn't enough in common between the two.
If the United States "falls," it will be for some of the same reasons that Rome fell, but not all.
The major reason for the "fall" of Rome was the fact that its empire had become too big to defend and to manage effectively. When this happened, there were all sorts of enemies waiting to invade the Empire.
You can argue that the US is overstretched. You can argue that the amount of money we spend defending the world is bankrupting us. If we fall due to this, it will be similar to the fall of Rome.
However, we are not likely to fall to invasion. Our "fall" would not be one where our country disintegrates. It would, instead, be one where we continue to exist, but not as such a great power.
In addition, much of our fall would be due to domestic issues. Our inability to decide how to reduce our budget deficits or make our economy more competitive would likely be instrumental in our fall in a way that was not true for Rome.