Rodgers' sack numbers don't get much better on 3rd down, but, even when adjusted for sacks, his Y/A on 3rd down is over 10 - by far the best in the league. The next best is Philip rivers at 8.3.
With that said, Aaron Rodgers has done a good chunk of his 3rd down damage when less than 7 yards remain. In fact, he continues to struggle when the team faces a 3rd and 8+ situation. (About 3.8 Y/A - including 5 sacks on only 30 attempts). However, on 3rd and less than 7, Rodgers has gone back to pass 28 times and has come away with a Y/A of 17.4 with only one sack.
I came in with a theory that Aaron Rodgers is good on third down because he has to make up for all the lost sack yardage from first and second down. However, while Rodgers does face more 3rd and longs than most QBs, his 3rd down rating is actually a result of big plays on 3rd and less than 8 yards remaining.