Trust Me

ASK FANTASY FLIGHT 

Q: If 'Trust Me' currently has 4 damage counters on it, can it still cancel an event?

A: You can attempt to deal 2 damage to the objective, but as per the rule on page 21 (under damage), damage in excess of a card's damage capacity is ignored. Because of this, the (full) cost of the cancel effect is not successfully paid, and the effect does not occur.