Push or fold in later stages or a tournament is all stack dependant. As you stack gets smaller waiting for premium cards goes away. It is part of a strategy that changes every hand as the antes go in. I just use my gut before i push and every one can limp and have me all in.
Its more that just
hands...
Is everyone playing for the money bubble?
Is there a lot of walks allowed?
What position are you? (How many players do you have to go through) yes I know the blind battle.
But as for hands I have pushed with 23o to AA. Depends on the situation.