Somewhere on the sheet add the formula =today(). This will let your
spreadsheet know what today's date is. From there you can simply add
Conditional Format to your selected date field. (Highlight the "due
date field" go to 'Format, Conditional Formatting, and enter as follows
CELL VALUE IS Greater Than (Whatever cell you put your =today()
formula.

This should give you your desired effect.

HTH

thanks for this Chuck, it works great. I've even found that I can set
up tasks that are due every other day by putting a -1 at the end of the
tag.