I just did the calculations, assuming a spare ship was kept in Miami and had to leave for Cozumel. This is 488 nautical miles and assuming a 'rescue' ship maintained 20 knots it would take them 21 hours to arrive on scene. This is not counting the time it would take to transition the ship's propulsion and electrical plant from what we former Navy snipes call 'cold iron' (shutdown) to operational status.
The U.S. military has some really big fleet tugs. They are now operated by civilian crews as part of the Military Sealift Command. Here is a photo of one.