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No, not generally possible in OmniFocus for an arbitrary date. But to some degree that wouldn't really give you a good answer anyhow, because you need to look at the surrounding dates' workload, too. If you have a big tax return marked as due April 15 (and not likely to all be done in one day), looking at your calendar for April 14 and OmniFocus and not seeing anything due April 14, would you be making a good choice agreeing to take on a substantial commitment that day? While I agree it would be nice to be able to filter for items that matched a specific date or date range, just like you can search for items containing a specific string, using it for this purpose seems potentially hazardous!

If you do want to do a search right now, you can use File->Export to toss your database into a spreadsheet and search it there.