vapor barrier is 6 mil, it's heavy enough, I found most painter drop sheets to be very flimsy in guage, closer to saran wrap than plastic sheet.
I believe you can get rolls of 2' wide vapor barrier (possibly black) for underneath/wrapping your 2x4 plates that touch the concrete floor, they may be cheaper than buying an entire roll of 6 mil vap barrier.
I think even a tarp cut into strips would work, as long as you have something that's a bit substantial it should do the trick.