It sounds like you are diluting the meaning of "due today" by having items with due dates where you don't really mean it. Some suggestions:
Don't put due dates on if you aren't serious about getting it done by the due date. Use start dates and a "tickler" perspective to manage those daily items instead. Context mode, group by start, close the groups for anything other than starts today. Your daily repeats will show up every day, and won't clutter up the due soon/overdue displays.
If you don't trust yourself without due dates, when you miss them for the daily repeats, immediately reschedule them to the next day so they aren't hiding these more important due soon items. You might also put the daily repeats in with a later due time than the real stuff, so you can do this step easily at the end of the day in a view where you've sorted by due -- the critical stuff that you still haven't gotten done won't be intermixed with the other stuff where you're just using due dates to try to prod yourself into action. You can use Dan Byler's excellent
Defer script to easily bump a collection of actions back a day.