Here's why:
* Subject vs. Object: "I" is the subject pronoun (the one performing the action), while "me" is the object pronoun (the one receiving the action).
* Prepositional Phrase: The phrase "to Mike and me" is a prepositional phrase, with "to" being the preposition. Object pronouns are used after prepositions.
Therefore, "me" is the correct pronoun in this sentence.