Saw an interesting look at stats from Football Outsiders recently. A reader asked about the 2009 Chargers, and if their offense had the greatest difference between passing offense and rushing offense in the history of FBO's stats (it was). They ranked first in the league in passing and last in rushing in 2009. A table showing the top ten offenses all time in terms of passing success/rushing failure was displayed. Of the ten teams, nine had winning records (the '08 Chargers finished 8-8). Eight of ten won at least ten games. Six of ten won 12 games. Without a doubt, it proved that you can win games having an elite passing offense and a mediocre rushing offense.
Because it makes sense in this context, FBO then looked at the teams with the biggest disparity the other way (great rushing offenses and terrible passing offenses). Of the ten teams, only one had a winning record. This team was the 2004 Falcons, with Michael Vick at the helm (obviously this team is weird historically and cannot be duplicated). The rest, including the 2000 Bengals (#2 team on the list), had losing records. In fact, only one other team even won seven games.
What does this all mean? You CAN win if you struggle to run the ball. You CANNOT win if you struggle to pass the ball (unless your quarterback is an unbelievable athlete in his athletic prime). If the 2010 Bengals want to continue their winning ways, they need to be able to pass the football. This means upgraded personnel and more importantly better playcalling.
Obviously, running and passing do not exist in a vacuum. In fact, better passing should lead to better running, and visa versa. However, running success should not come at the expense of passing success. All historical trends point towards this being foolhardy.