Here's why:
* Prepositional Phrase: A prepositional phrase starts with a preposition (like "to", "in", "on", "at", etc.) and ends with a noun or pronoun (the object of the preposition).
* Preposition: In this case, the preposition is "to".
* Object of the Preposition: The object of the preposition is "her deadline".
Therefore, the entire phrase "to meet her deadline" acts as a prepositional phrase modifying the verb "worked".