Do National team F.A's ever make demands to their manager?

i.e do they ever demand you select a certain player that you constantly overlook, or do they refuse to allow a certain player to be appointed captain, or if you fell out with a star player who walked out of a tournament, would they sack you to appease him?

I think it would be good to improve the role International F.A's play in the game, because from my experience of international football, they don't do anything-apart from saying things like they're satisfied when you win the world cup, or just sack you if you ever dont win eveything if you're Brazil!