In "The Road" the father would do anything for his son. Even though they are faced with adversary the father would do anything for his son, he reads his son a book, gives the boy the only Coke that is left in the store. When they get enough oil, the father leaves the light on, knowing that it will burn the oil supply and it will be harder the next time they need light, just because his son asked him to do so. The father would do anything in order to give his son a normal life, especially since the boy doesn't know anything other than this. He was born into the carnage, but the father wants to raise his son the same way he would have without the wreckage, as long as he is keeping his son safe.
I feel that today's fathers would do the same as the father in "The Road", but not to the full extent. The fathers today wouldn't give the entire Coke to their child, they would most likely blow out the flame to conserve the oil for a time when they really needed it, also they probably wouldn't read a book to their child just because there isn't enough time or today's fathers wouldn't think it's a necessity.
