Should felt paper overhang an eave drip edge?
There is no need to overhang the felt underlayment. If you do, it will sag and look sloppy. The important part is to make sure you have the correct overhang of shingles. I usually leave about 1/2-3/4" overhang, even when there is a drip edge.

Here are some FEMA Roofing Guidelines.