Have you actually tried the syntax #due(5 days) or #due(1 week) etc, that should be supported and should give more or less what you want. You can also save this as a smart overview (premium feature). In other words, what we don’t support is “this week” type queries, but we do support “the next x days, x weeks or x months” type queries, which at the start of the week would allow you to see everything for that week.
For completion sake, here’s the kind of queries we support at this moment:
#due(today)
#due(yesterday)
#due(friday)
#due(1 day)
#due(5 days)
#due(-1 day)
#due(1 week)
#due(2 weeks)
#due(3 months)
#due(5 days ago)
#due(1 month ago)