What does “Mitt Romney pretends to be a Nascar, cheesy-grits guy” mean?
...apparently that's what them good ole boys down in Texas eat when they get back from an afternoon at the stock car racing. Mitt Romney - just an ordinary guy like all the voters (except he has a bit more money than most of them!)
EDIT: The question has arisen in comments as to exactly how Dowd's phrasing represents stereotyping. I'm a Brit who's never been to a stock car race or eaten "grits" - or even heard of NASCAR and "cheesy grits" before. Nevertheless, I grasped the sense immediately.
To my mind that makes it axiomatically a "stereotype", even if the specific referents used to invoke it are unknown to me (and probably never used in that conjunction before by any other writer in history). It's true Romney recently went to a stock car racing event (he fluffed that by saying his interest in the sport was proven by the fact that one of his friends owned a racing team). And he recently claimed he liked eating "grits" (a dish strongly associated with poor Southerners, and about as likely as Bill Gates tucking into Pot Noodle/Cup o' Noodles every night).
As a "journalist/media pundit", Dowd wouldn't want her words open to being challenged on factual grounds, but the average reader doesn't need to know or care whether the specific allusions have any basis in Romney's recent activities. All that matters is we understand Dowd to be saying Romney falsely claims to be a stereotypical ordinary guy just like those whose votes he seeks.
Maureen Dowd is basically accusing Mitt of pandering to southern voters by pretending to like the same things they do: NASCAR and cheesy grits, both of which are stereotypically southern sorts of things.