There are a lot of current and recent NFL quarterbacks that could be great ones if they had time to set their feet and throw while untouched in the pocket. Unfortunately for them, the reality is that if they can't react and produce while under pressure, they won't have a long career as a starter in the NFL.
I was surprised by an article last month that didn't appear to consider Green Bay Packers QB Aaron Rodgers as a great one under pressure. I think he does an outstanding job at avoiding pressure and throwing on the run. Most APC readers agreed in the poll conducted last month.
First, Rodgers was one of the least pressured QBs last season, with approximately 28% of his drop backs resulting in pressure. As they noted, that stat is based on how well his pass protection performed and how quickly he got rid of the ball. Both he and his offensive line deserve credit for a great season.
Second, his completion and sack percentages when pressured was average. That's not surprising because his style is aggressive and he doesn't throw to his checkdown receiver too often.
Third, he was average on the ratio of touchdowns to interceptions when under pressure. In this stat, Falcons QB Matt Ryan has no equal. But Rodgers was in good company with Peyton Manning and Matt Hasselbeck rated just above him, and Jay Cutler and Drew Brees rated just behind him.
Fourth was how he did under pressure based on Pro Football Focus's own rating system. And he had their highest rating when under pressure.
That doesn't mean he's perfect or clearly the best, but it's certain that he's among the best when under pressure.