I haven't seen No Country For Old Men, but isn't it one of these?
Movies where sort of average guys find themselves in a violent armed conflict. And they turn out to be pretty good at it.
What are examples?
Bring Me the Head of Alfredo Garcia, where a piano player mentions that used to shoot guns a lot, and he finds himself shooting it out all over the place. Sam Peckinpah. Well worth watching (even though Harry Medved, half-brother of effeminate right-wing talk show host Michael Medved, listed it as one of the fifty worse movies of all time.)
A much milder case was Gene Wilder in Silver Streak. A guy traveling by train because he's afraid to fly has to battle violent criminals with a history of attacking public transportation.
Another Sam Peckinpah movie, Straw Dogs with Dustin Hoffman as a mild-mannered math professor who battles over-charging English workmen.
And another Dustin Hoffman movie, Marathon Man where a middle aged jogger/college student battles Nazism with his father's suicide weapon.
There was Three Days of the Condor where a mild mannered CIA analyst battles the federal government.
In a somewhat similar vein, the James Bond movies that I thought worked were the ones that started with James Bond in the office being treated rather badly by his superiors around the office until he finally gets out in "the field" and can do what he likes. The ones that stand out in my mind in this regard are Dr No which starts with him being forced to trade in his gun, Goldfinger, where Q is rude to him while showing him the new gadgets, Never Say Never Again where M actually seems to hate him.
I'm sitting here now watching Breaking Bad. Walt seems to be developing a capacity for violence, but who knows.