How long before it actually dies?
If this was a question that could actually be answered, the warning would be "you have xx days, xx hours, xx minutes until your battery dies," rather than the current wording. And if Tesla can't put any more of an accurate number to it, I don't think us forum jockeys will be able to do much better.

I'm not trying to sound like a jerk here, it's just the way it is.
Unfortunately, the failure modes of lead acid battery are such that often times a warning simply isn't possible, and even when a warning *is* possible, it means you have between zero hours and xxxx hours until it dies.
If you're unable to get it changed in a reasonable amount of time, you can keep the car "awake" from now until you can get the battery changed. There are quite a few good posts/threads about how to do this, but a quick and dirty method is to hook your car up to your Wall Connector and turn on the climate control to a reasonable value... one that's not too far from the ambient temperature of where the car is parked to avoid using too much energy. If using the climate control would deplete energy faster than your available charging source can replace it,
there are alternate means of keeping the car awake, but come with various caveats. If possible, leave the climate control on until you get the battery changed.
My own caveat: It has been a while since I've read the latest regarding how a car can be reliably kept awake, so it is well worth the time to research this a bit more.
I'm sure that others will respond with turning Sentry Mode on, but there are caveats to this method, as well. These can be found by looking around a bit.

Leaving the Climate Control on is an absolute, sure fire way to make sure that the car doesn't go to sleep. It's worth restating that you need to make sure that your charging source can replace the energy the climate control is using faster than the car is actually using it.
Keeping the car awake will mean that the DC to DC convertor will power the 12v system, so that the 12 volt battery isn't used. The 12 volt battery is only used while the car is asleep, and is also used to switch the car from "asleep" to "awake" states.