Most of the time if there is vibration the bit will be the culprit and either it has been damaged or it's out of balance. If it's out of balance that bad then chances are it's a cheapo. If you get a 2" or larger bit that's out of balance it can get downright scary when it gets up to speed.
Someone I consider a master woodworker once told me that a master woodworker is not someone who never makes mistakes. He is someone who is able to cover them up so that no one can tell.