Can a trade in be repossessed

Okay guys need some input please. I recently went to a dealership and traded in my car and got a new car. New car loan etc. The dealership will be paying off the remaining $1500 on my old car loan. I have been driving my new car for a week now. Also I signed over ownership of my old car to the dealer. I just got a call from my old car loan company that they spoke with the dealership and apparently it will take 30 days for them to get their pay off check. The lady said they dont want to wait that long and if I dont make a payment they will go to the dealership and repossess the old car. My question is can they do that and if they do can I lose my new car?? Thanks so much for the help guys