Admittedly I don't watch the Cowboys unless they're playing the Bears or on the Sunday night game, but whenever I do watch it seems like Romo's inconsistency is due to his own screwups as much as it is due to the rest of the team's shortcomings.
Looking at some statistics ... Romo is sixth among active quarterbacks in fourth-quarter comebacks and eighth in game-winning drives. In close games (0 - 7 point margin), Romo has a career 91.3 QB rating. In November-December (the months the media claim Romo chokes in), he has a TD:INT ratio of 99 to 40. And he has a passer rating of 90 or higher against seven of eight NFL divisions (86.3 against AFC North).
Basically, with quarterbacks right now, you have the top tier with Brees / Rodgers / Peyton / Brady, people who always seem to be on and a bad game is a rare sight from them. After that, you go to a second tier with Eli, Rivers, Romo, Roethlisberger, Ryan, Flacco, and you could make a weak argument for Cutler.
So, Romo isn't a demigod like Brady, but he's far from being middle of the road, too. Like I said, if the Cowboys didn't give him this deal, someone else gladly would have; I can think of probably a dozen teams that would give up anyone on their roster to have Romo under center.
In any event, Romo has zero buttfumbles in his career, so he can get whatever he wants.