How to tell DS that there's exactly zero chance that his girlfriend can stay here at Thanksgiving?

Yes.
When 2 people are married, there is a financial obligation/contract. Even without financial obligation, there is a sense of “for better or for worse,” in trying to work out whatever issues you may have. If you are not ready to make that commitment yet then it is better to have a place you could go back to just in case. I would not want my kids to stay in a living situation with someone just because they didn’t have a place to go to - save that for marriage.