I would experiment, but start at med pressure and 4 depth. Construction paper doesn't have a much of a shelf life in the long term so if you are doing something you want to keep, I'd switch to archival paper. If you're doing locker tags or something similar, go for it!
Amanda construction paper is not that thick. I agree with Marlene, medium depth and 4 sounds about right. Try it out on scraps of construction paper first. Good luck!
Thanks ladies! I work in a preschool and I'm using Everyday Paperdolls to create name tags and I got multicultural construction paper. I couldn't find very nice skin tone shades in cardstock!!! =) I'm doing the clothes from pp and such...I have an old mat I'll use and just tape the c.p. down on the edges. =)
I would just watch your blade housing....construction paper is very fibrous (sp?) and it may get into the housing. You could just take a can of pressurized air and blow it out when your done.