You may not get a response if you are not selected. Depending on the site, there may be a way for you to see who, if anyone, is selected.
I use eLance to hire people sometimes and it used to be set up so that you could click to turn down people, and it gave you reasons to pick from (Like too expensive, preferred another method, did not address issue, etc.) But now I notice there is no way to contact the bidders unless you go into each one and send them a private message. I feel bad just ignoring people but I figure that's the way it is set up now and the people bidding understand that. That is eLance. I don't know about other freelance sites.
Regardless, I would not expect a response within a day.