I'm no expert, but from what I've read, cold war era ICBM's from the former Soviet Union had an estimated travel time of 20 minutes to reach the Continental (northern) United States. If a U.S. interceptor did try to shoot down the aircraft, I'm guessing that it would have to be a far shot so as not to get shot down themselves and the window of oppurtunity would be very short (seconds) because the missile would be accelerating up to speeds in excess of Mach 20.
If an F-14 Launched a Phoenix after it aquired the missile and locked (say from 10 miles), I think the ICBM would outrun it!
Sorry... meant to type ICBM.