A healthy Romo doesn't guarantee squat. Again I'll point to the 1-5 record the Cowboys had in 2010 in games that Romo started. If the roster is bad he's not good enough to make up for the short comings. Especially with his bad back.
The offensive supporting cast was bad in 2010.
That offensive line was truly offensive and Marion Barber was done, though they still paid him like a top-5 RB. Net result was no running game and frighteningly less time to throw, especially early on with Marc Colombo out of the lineup. With the line in shambles, the draw play that worked so well between the 20's in 2009 was non-existent in 2010.
The biggest problem was Jason Garrett's abject refusal to stop passing while Wade was coaching. The minute Wade was out, RHG started running the football and suddenly the team was almost competitive again to finish 5-3.
So it wasn't really Romo, it was RHG going pass-happy because he had Romo-- basically forgetting that football is a team sport.