Yes its possible but youll have to max out most skills to reach the required level. The level cap is 81 and theres a quest that gives 5 bonus perks so maximum potential is 85 perks. That covers a full third of the perks in the game, so you could max out Mage perks, or Thief perks or Warrior perks... or go for a mix of them all, obviously.
Level 50 for perks, 70 for max level.
Utterly outdated info. You keep gaining perks up to the end, and the max level is actually 81.