As an American, my tourist visa for Germany expires December 22. However, I'm turning in my application for a work visa this week. While I wait for visa approval, do I have to stay (thus receiving some form of temporary visa or something), or do I have to leave and wait for approval from my local consulate?
You can stay in Germany, until your application has been processed, see § 81 Abs. 3 Satz 1 AufenthG:
If a foreigner who is legally resident in the federal territory and does not possess a residence title applies for a residence title, his or her residence shall be deemed to be permitted up to the time of the decision by the foreigners authority.
To certify this right you get a Fiktionsbescheinigung when you apply, Abs. 6:
The foreigner shall be issued a certificate confirming the effect of his or her application (provisional residence document).
This does not allow you to work during that time .