It could be any time at all, including never.
I think that as soon as possible can be within a week, or less. I mean, it depends on what it is, but it usually depends on the person and how long it will take them to get back to you. For instance, if it's for a party, they might need time to think about it and check their calender. So, I think it could be soon, or as soon as the person thinks is as soon as possible.
== Answer ==
When this response is given, perhaps a clearer way to deal with it would be to say "When can I check back with you, Monday, or would Wednesday be better?". [Or whatever timeframe is workable]
Emdrgreg