To be honest I always assumed that they hunted down survivors with their fighters. Afterall their goal was to extermiate humanity, we did not see smaller scale attack on screen but that don't mean they did not happen. And add that with starvation lack of sanitization and epidemy and the dead toll would increase a lot, and let's not forget countries who were dependent on foreign aid to feed themselve. Imagine the mess of milions or even billions of refugees in unsanitized camps always on the look out for an incoming attack. Evacuating cities does not mean you are safe afterall until the counter-attack the aliens had complete air supremacy over the Earth.I saw an interview somewhere where Sela Ward says the death toll was three billion, which seems... impossibly excessive.
I've always felt comfortable with "hundreds of millions" as mentioned at the end of the novelization. That seems to square well with how the first 36 targets probably suffered huge casualty rates, and any cities still standing at that point were probably deserted shortly thereafter.
If the death toll is 3 billions it basically cut the 1996 earth poppulation by half.