P.S. Oh... although we haven't specified that you can't do this for attack rolls, no one has ever used it for that because it just seems a little silly.
The problem with trying to use with attack rolls and saving throws is that a 1 is an automatic failure and by using this rule you eliminate that specific issue. I wouldn't allow it because of this one.
Rules that use Action Points also specify that you can't use them to modify a nat 1 on an attack or saving throw.