We have seen how the Spanish conquistadors were able to bring down large empires in North and South America with a handful of men. Jared Diamond...

This is, of course, a matter of opinion and conjecture as nothing like this has happened in any culture in a very long time and nothing even remotely like this has ever happened to the United States.  My own view is that the answers to these two questions depend very much upon the exact circumstances in which we found ourselves.

In general, I believe that we would have a better chance at mounting a defense and at holding our society together than the Aztecs or the Inca did.  This is because elites do not dominate our society in the same way that they dominated those societies.  For example, imagine that the president and half of Congress died.  This would disrupt things of course, but we would have many other leaders who would be ready to step in.  We would not descend into Civil War over who the next president would be because we have laws that govern these sorts of things.  We would not be lost because there are any number of our citizens who could step into government positions and be able to lead.  Our culture is more democratic than theirs and so the deaths of half of our leaders would not impact us as much as it impacted them.

Looking at specific situations, I believe that we would be more able to mount a defense if we knew the cause of the deaths.  If people just seemed to be dying at random, with no symptoms, it would surely cause panic.  However, if people started dying from disease, it would not destroy our social fabric as badly as it did that of the Incas or Aztecs.  We would be able to understand what caused the disease.  We would have a hope of finding a cure.  We would not be helpless like people were in those days, thinking only that it was the will of the gods that people were dying.  So, the more we knew about why people were dying, the better our society would hold together, even if we had not yet found a way to prevent the deaths.

In addition, our ability to mount a defense would depend tremendously on the power of the invaders.  We would surely be destroyed if we had people invade us, say from outer space, who were as far ahead of us in technology as Europeans were ahead of the Native Americans.  We would be able to mount a defense, but it would not matter all that much because even our best defense would not be able to prevail against them.  However, if we were attacked by someone more on our own level, I would think that we would be able to defend relatively well because we would still be motivated to repel them (unless we thought they could prevent the deaths, in which case we would probably give in).

In general, then, I think that our society would not be as badly affected by these deaths as the Incas and the Aztecs were.  This may simply be my own bias because I think we are so much more advanced than they were in every way.  I believe that our social fabric would not be ripped apart as much as theirs because we have much more scientific knowledge and we have a society that is much less dominated by political and religious elites.