Yes, girls cooling off will happen sometimes... especially when there's a delay until the date. Sadly.
You should try to choose an approach based on your read of how well things went with her. If you made a strong first impression and she clearly liked you, use the delay tactic I mentioned in my response to Ben (commenter above).
If you think she may cool off though (impression not as strong; she seemed busy or more business-like), it may work better to have some interim communication. If you get a strong "this girl's going to cool off" vibe, you may not have made a strong enough impression -- where that's the case, phone calls help a lot. In cases like that, it can be worthwhile to set the date, then a few days in call her up and either have a quick chat or leave a little voice mail in your sexy phone voice.
With girls who don't reply to schedulers: I have done the research, yes!
I used to do the 'witty/interesting text after a few days' without a date request in it. I found girls will often reply to this. Often with an apology for not responding to your earlier request. However, it almost never leads to anything. They don't want to brush you off when they see you're fun/interesting/cool, but they don't want to date you either.
I have had success with switching to phone calls though -- I recommend that. Even if she doesn't pick up, if you leave a great voicemail the "phone paranoid" girls will sometimes respond via text and you can set a date up with them then (once they've heard your voice and remembered they like you). If you can get them on the phone obviously that's even better. Usually it is an 'on the fence' thing; if you can give her some extra things to feel good about you with (like your vocal tonality, your comfort on the phone with her, the laughs she experiences in a call with you, etc.) that can be enough.
The other option you have is to write her off as a one-on-one date candidate, and invite her to a party later. This can work. The weird thing that will often happen is
She ignores your scheduler text
A week or two later you invite her to a party
She apologizes for not responding to your scheduler text, tells you she can't make the party, then offers you her schedule for the one-on-one date
Seems to mostly be a social proof / social value thing. She sees you're a guy with an active social life, decides "Oh! I guess he's okay then", and opts to go out with you at that point.
So, those are your two best options for girls who flat-out ignore the scheduler, in my experience: call her up, or party invite her.