The scene glosses over the reality of the situation. The aliens destroyed the cities of New York, Los Angeles, Houston and Washington DC with their opening salvo. The humans nuked the strikeship in Houston with no effect to the strikeship, but plenty of effect to the surrounding countryside. After the initial attack, the strikeships started moving through out the country, destroying major cities. We could probably add Boston, Philadelphia, and Las Vegas, NV to the list, at least. The rest of the world fared no better, with all the major capitals destroyed, followed by subsequent destruction of major cities.
The power grid was probably destroyed, so most US cities have no power. The refineries near Houston were destroyed also, so gasoline would soon be in short supply. Food could not get from the farms to the survivors easily. The catastrophe grows greater the more you think of it.
And the aliens could have done so much more. Fortunately for us they were a telepathic race with no concept of internet security. Any sort of smart alien invasion we would have little chance against. Most stories of alien invasion deliberately gimp the aliens so humans can take that slender shot, and against all the odds, triumph.I'm all for humans winning, but we may not be so fortunate as our fictional counterparts if we ever contact intelligent alien life.Luckily for us, it appears we have a long time (possibly forever) to prepare.