chris,
You've set the game in the 1970s. This makes using the cold war incredibly obvious, especially because you're not using the hyper-50s stylized feel of X-Com. Your tone looks more period-authentic, which probably makes everyone think of the cold war. It jumps out at me that you're not using it: It feels like something's missing.
What if the already ever-present threat of nuclear armageddon appeared to be a constant risk. Score poorly one month, and you'll get messages about increasing geopolitical instability. In addition to the random cropcircle and storm events, there would be random events relating to the world's political situation. Wars, assasinations, terrorist strikes, and so on. They don't really mean anything, but they are an indicator that something is wrong. Aliens could have missions designed to worsen the global situation, as well. The main point is that nuclear war could save a player from a game that's doomed to failure. When the player does worse, and worse, and worse, the odds of a nuclear exchange grow higher, effectively putting the game out of its misery.
In reality, it would simply be the game saving you from a 20 hour long death spiral. It causes no real additional complication to the game... it only seems like it does. It would look to the player, however, like nuclear war was the entire point of you setting it in the 1970s. The world ended. Nuclear War. Aliens caused it.