Since Aaron Rodgers' first year as a starter the Packers team rankings as far as points scored per game in the regular season from 2008 through the first 6 weeks of this season are (in order) : 5th, 3rd, 10th, 1st, and 10th. So they've been in the top 10 every season.
The average number of rushing attempts per game over that span is 25.9, with a high of 27.4 and low of 23.8. Their average per rush is 4 yards, with a high of 4.3 and a low of 3.8. This season the Packers are averaging 23.8 rushes per game for a 4.1 per attempt average. The Packers most prolific offense was last seasons': In order to match the rushing attempts per game this season to that team they would have had to run the ball one more time per game. To reach their average over this period of time, they would have had to run the ball twice more per game. So it's not as though the Packers run/pass mix has been way out of sync regarding their average since Rodgers has been QB. BTW, their average per rush is 4.1 yards this year vs. 3.9 last season which is the second lowest average per rush over that time span.
As I've posted (perhaps too) many times, IMO what is necessary for McCarthy's offense to succeed is that they present a credible threat of a run in order to keep defenses off balance. Of course there are other ways to keep Ds honest and slow down a pass rush: Traditional screen passes, bubble screens, shovel passes, quick slants, check downs, bootlegs, and even having a QB athletic enough to hurt Ds with his feet. There's no way for me to measure those alternative measures and no statistical analysis is close to perfect anyway. But IMO the point these stats make goes along with my observations: The success of the Packers offense depends mainly upon the efficiency and consistency their passing game. Running the ball one more time per game to this point wouldn't have made a significant difference.
IMO the recipe for winning is to have Aaron Rodgers and his teammates on offense return to their incredible play in the passing game, to run the ball about 24-25 times per game and to have the defense play with the intensity they did Sunday night.
(I used team stats from nfl.com and I did some of the math above.)