Jamie, you do need to be careful if you use plastic that it doesn't touch the leaves of the plants, as it will conduct the cold, and also burn the leaves if the sun shines on it. You'd need to get out and vent your tunnel on warm, sunny days for the same reason. The plants easily get too warm with direct sun through plastic.
Maybe start out with plastic, then graduate to using frost cloth as the weather warms? I got what I think was a good deal on sheets of frost cloth from Gardener's Supply. They sell it in up to 6 x 50ft. sheets.
To be sure you're keeping the edges down in the wind, I sewed wide hems along the edges and slid heavy bamboo poles into them. (I have lots of bamboo) You could use pipe, rebar, or wood, whatever you've got lying around that is heavy enough.
