Now, that would be rock bottom wouldn't it?
If by "rock bottom" you mean "a thousand years of darkness", then yes.
I don't know if it would take us a thousand. We'd have the rest of the world to keep technological knowledge, etc., alive.
Very plausibly we'd lose about 2/3rds to 3/4ths of our population, though. We'd cease being "the United States of America" for some time.