Here's why:
* Prepositional Phrases: The phrase "with Mike and me" is a prepositional phrase, with "with" being the preposition.
* Object of the Preposition: The object of a preposition is the noun or pronoun that follows the preposition and receives its action. In this case, "Mike and me" are the objects of the preposition "with".
* Pronoun Case: When pronouns are used as objects of prepositions, they should be in the objective case. This is why "me" is used instead of "I".
Therefore, the correct sentence is: "You should come to the party with Mike and me."