Firstly, same day don't even bother trying with an independent even if they say "same-day availability". If you want to see someone within the next 8-10 hours contact an agency. There a number of reputable ones that will hook you up in short notice. God bless them. I remember Elsi had a same-day charge that I respected because I knew she'd pull through, and I'd never get any grief for being an unprepared perv.
Second, for independents I usually give a loose 24 hour turn around time. I know some of them only do their messages *once* per day. I know they have lives and boundaries which should be expected. I also expect that if the turn around is the equivalent of a blind carrier pigeon that circumstances change, and an previously stated availability for myself might not be available anymore. Mutual respect right? I also expect everyone to be vying for the attention of multiple clients/providers, this is Vancouver after all. That's just business. So fire out as many inquires at once as you want, there's no point in playing the message tennis with a single provider.
Thirdly, if you find that provider that has your fancy, it really doesn't matter how much time it takes then.