Heres one to chew on, its explained that the Soviet Union needs the US mostly intact, because of food shortages in their own territory, so it makes sense that the United States isn't just a charred wasteland. But the US forces are under no such restriction. Now apparently they got most of our land based silosnote Which on its own makes no sense either since those silos would have launched as soon as the inbound missiles were detected but last I checked in 1985 the US had a pretty large submarine force, most of which is armed with nukes. One would think the first order of the day would have been, waste Moscow, and any other major Soviet city, and probably some Mexican and Cuban cities as well. The first reasonable explanation is of course the war in the movie would have lasted a few weeks or even more likely hours when the invaders learned that their homelands were a charred wastelands and any hope of supplies or support had burned with them and either decide to go on a suicide attack or surrender. However, there is a perfectly possible explanation for the lack of a US nuclear retaliation. The United States government was unwilling to order a genocidal attack even when faced with a war which would end with many civilian and military deaths and would rather risk losing the war and suffer the casualties for waging a conventional war then be responsible for killing billions and causing all kinds of ecological disasters. Also, the lack of a US nuclear retaliation might help shift world opinion in their favor, causing other countries to at least support the US cause if not outright join in the war effort on their side.
On top of that, the invasion is stated to have started with Decapitation strikes on American command and control centers committed by infiltrators. By the time the American command chain had been reestablished, it was too late to launch nukes without risking retaliation and they likely didn't want to risk escalating the war further.