I'm pretty sure this is Tetragnatha viridis Walckenaer, or Green longjawed orbweaver. The red patch at the front of the abdomen was the give-away since I can't see the eye pattern or mouthparts. According to Common Spiders of North America, they're "found along the East Coast and in the Southeast. They are a spider of pine forests and occasionally other conifers. The web is built in the low branches of pine trees."
It is very exciting to receive a spider sighting this time of year - especially one in bright green wrapping paper. Thanks, Gudrun.