I don't think contacting Apple Support is going to help much, but you can always give that a shot.
Clearly the error message acknowledges a known (to them) issue and a response saying you need to wait days for them to have a fix.
Initially I heard mostly from UK and other EU users so I guessed perhaps Apple needs to cleaning up those accounts. I don't think this anymore since it looks like some portion of people across the globe are being delayed.
Each user that signs up for Apple Music causes server load:
- CPU and network bandwidth is needed to communicate with their devices
- Each user uses storage and has to have their preferences recorded and playlists generated for each user (or at least linked to their accounts)
- Each user's iTunes library needs to be ingested and stored online
If Apple has a temporary capacity issue, code scaling issue, or their model for how many people would sign up were too conservative then it might take days to spin up more servers or test and deploy the code change.
I've heard one person try to make a new Apple ID. I'd strongly recommend to not make a new Apple ID unless you are prepared for even more confusion or clean up later. If you're desperate to try the new hotness this weekend, you can always open a support ticket with Apple or if you feel this error message shouldn't apply to your account.
My guess is this is an evolution of this error with an explanation that you don't need to do anything other than wait a day or so...
You may have to pay for support if AppleCare don't see this as something that's in their scope of free support (recent purchase, paid AppleCare or just free to ask for anyone):
Look for an updated FAQ and articles or use the "Contact Us" link on the left if this drags on past your patience in the matter. I hope the delay is short for anyone wanting in on the service.