The Bible tells us that Jesus was born during the reign of Herod the Great. Herod died in 4 B.C., so Jesus had to be born before that.
Mathew 2:13-19 tells us that an angel told Joseph to take the mother and child to Egypt where they lived until the death of Herod. This tells me that Jesus must have been 2 or 3 years old when Herod died. Adding all of this up causes me to believe that Jesus had to have been born somewhere between 7 and 5 B.C.
He certainly could not have been born in 3 B.C.