Verification failed there was an error connecting to the apple id server - iPhone

I'm on vacation out of the country and suddenly I'm unable to connect to the internet, get iMessage, email, ect... These features were working previous but just stopped out of nowhere- it had been working fine for 3 days.

I am connected to the local wifi network and given a password from the hotel to enter once safari opened up. Data is turned off, voice roaming only, ect..

I need access to work emails otherwise I'd hold of. I've read though other forums but nothing has worked, short of resetting my whole device. I've also attempted to back up to my iTunes/icloud on my macbook. Any help would be greatly appreciated!