Big water leak originating in my unit caused damage in the building – how urgent is it to start repairs?

The hot water heater in my condo blew a gasket this morning and the water flooded out of my unit, into the unit below me and into the hallway below that. The condo is in DC, rented out, and I live in California. The plumbers called in today (Michael & Son) to address the emergency are insisting that remediation MUST start within 24 -48 hours or there will be terrible mold etc. They have not provided a quote for any of that work saying "The reason we wait until the work is complete is that restoration is a dynamic process." The quote they gave to replace my water heater (over $4K) seems exorbitant, so I'm not exactly filled with trust. My preference would be to get several quotes and determine what my insurance company will pay before starting. Any thoughts on whether the damage is likely to become that much more severe if they start Monday instead of tomorrow?