Seeing a pledge (or recurring gift) as overdue on the day that the payment is scheduled is not particularly helpful. It would be better to have a configuration screen for tags where you could set any related tolerances e.g. being able to set the appearance of the tag to be no earlier than # days after the payment was scheduled.
This change would allow fundraisers to concentrate on items of significance, rather than the "background noise" of slight mis-timings of payments etc.