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Whether done automagically, like in ToodleDo, or manually, like in OmniFocus, how well this scheme works is going to depend on how serious you are about due dates. If you use due dates for things that aren't really due, there's going to be some distortion in your system.

With OmniFocus on the iPad, I would suggest using the Forecast view. Each day, try to complete anything that is due that day, plus anything that is overdue (*). Remaining time and effort can be spent knocking off tasks due in the next few days, tasks you've flagged during your reviews, and tasks that are newly available. If there isn't enough time to do everything, you make your decisions without having them scrambled about by the evaluation function.

(*) Here's where the bit about due dates comes into play. If your due dates are real, then you're going to be more committed to getting them done. If a lot of those due dates don't really have any repercussions for missing them (or letting them slide once you've missed them), you'll accumulate overdue actions and some of the utility of the system will be lost (more so for ToodleDo than OmniFocus, I think). I speak from experience on this!