The widespread support for resisting the Tea Act had more to do with principles. By buying tea, even though it was cheaper, colonists would be paying the duty and thereby implicitly acknowledging Parliament’s right to tax them.
This showed the colonists truly cared about being free from the power from the King of Britain, because even though it was in practice actually cheaper for them now, because of their principles they decided that they wouldn't support anything that showed Britain that they gave in to his power.