You're definitely not screwed, it just takes a little bit of setup/pre-planning. You're actually not alone, there are a decent amount of van/RV life people out there that use cpap machines. I've even talked to two people that use them in their prius living setups. I plan on setting one up in my van as well.
It's mostly just a matter of having enough power. Can you give some more details on your setup? Do you have extra batteries/solar?
I would first get one of those kill-a-watt devices to see how much electricity your cpap takes over the course of 8 hours or so. I got one of these to measure the wattage on my laptop and microwave i want to put in the van:
it's about 18 bucks or so. Use that to measure the wattage of the cpap for about an hour. Then multiply that by how many hours you sleep (8-10) then you should have the amount of amps it uses per night (i.e. 20 amp hours, or ah). Get a battery (and inverter) that lasts twice as many amp-hours if it's a deep cycle (since you never want to drain a deep cycle past 50%) or one that's near what you plan to use if it's a lithium battery and can recharge it every night. Obviously the more amp hours the battery has the less you have to recharge it.
I'd have some kind of hookup to your engine/alternator so it recharges when you're driving around if you don't have solar.
A portable battery bank like the Jackery 500 or something similar would be ideal for this kind of setup since it has an inverter built in.
Either way, battery/solar setups are a larger discussion, but to answer your question, a cpap machine in a vehicle living setup is completely do-able. Let me know if you need more details.