Your screws are definitely too long if that's the case. There should be no screws sticking out. It sounds like you already purchased your plywood, but if you're looking for a slightly more portable solution, I highly recommend the table featured in this video:
We built it 2 weeks ago, and it's really nice. If you (or anyone else on the list) has questions about how to build it, feel free to contact me off-list. Total cost (including a doweling jig) was just under $200. Not included in that figure is a power drill and a circular saw.