That is, was there ever a specific fictional book or film about an American/NATO invasion that similarly caught the contemporary popular imagination in the USSR?
This is about as close as it gets, as far as I know: http://www.imdb.com/title/tt0085723/ English title: Incident at Map Grid 36-80
Had to Google the name of the film (and ended up finding it through a Yahoo Answers question, of all things), but a former professor told me this was about as close as it got. For the most part, Soviet films were about how great the Soviets were, their long tradition of overcoming adversity, and the promise of a future ahead. The few I've seen didn't have a particularly bright future, at least not in Western terms, but the idea was that the USSR would continue on in perpetuity.
Also, the US Military tends to style itself as the "Blue" force and to the best of my knowledge the Soviets called them the same. Sounds nitpicky, but it's more of a curiosity than anything else. I've always wondered about the difference in self-styled colors/standards and how other forces label each other, but I'd imagine that's a paper whose priority to be written is pretty far down the totem pole.
Note/disclaimer: Though I study military/defense issues, I'm not a Soviet culture expert.
Edit: Did a little more poking around and found a Wikipedia page on the movie: http://en.wikipedia.org/wiki/Incident_at_Map_Grid_36-80 and analysis from the Harriman Institute at Columbia: http://harriman.columbia.edu/event/screening-mikhail-tumanishvilis-%E2%80%9Cincident-map-grid-36-80%E2%80%9D
Not sure I agree with the characterization on the wiki page of it being equivalent to Rambo II, but the claim that the film was pretty typical in making the good guys look awesome and the bad guys look incompetent fits. The Columbia synopsis is even better.
Not a direct answer to your question, but I thought you might find it interesting as it is somewhat related.
There was a large number of soviet made western movies. These films were quite different from their non-soviet counterparts. In the soviet westerns, we saw the good communal indians fighting the evil capitalist cowboys.
The only "Invasion of Russia" type movie that I know was made was "Alexander Nevsky" by Sergei M. Eisenstein. Of course that features invading Teutonic Knights (symbolizing the evil Germanic horde of 1939) which was much more frightening (and turned out to be rather more realistic than the Soviets wished) than NATO ever was during the Cold War.
Why are you associating the US with the color white? Is there some significance behind it?