The book is set in January 2021, but apart from that I don't think there are any dates mentioned. So that date is theoretically possible but highly unlikely. More probably the movie's got a different date. (It's been a while since I've seen the movie; I prefer the book immensely.)
It always fascinates me to see how sci-fi writers' predictions come true (or don't) based on their timelines. In this case, it was 53 years ahead of the Space Race, so we'd of course already colonized Mars. We've still got a couple of years on that one, but I think we're going to miss the mark. On the bright side, we haven't had the great Atomic-Era fear of World War Terminus that's made the planet a barren wasteland, so that's something. I wasn't really looking forward to having to wear a lead codpiece around all day.