This is what I do. No tables big enough.
Buy an appropriate size cheap plastic table cloth with the soft back
Run it in your dryer on low for a few minutes. Keep check so it doesn't get too hot. While still warm spread it out on your carpet with the vinyl side down. Smooth it all around.
Using spray starch, I like Niagra Non-Aerosol in the pump bottle. Biodegradable. Lightly dampen the the back side a little at a time while laying the quilt backing down. and smoothing the backing as you go.I use a low heat iron to lightly press keeping the fabric smooth.
Do the same with the batting,spraying,smoothing, DO NOT IRON
Lay the quilt top on the sprayed batting. Ok to press it.
This is my favorite part. When trimming the three pieces to size, cut through the vinyl table cloth> this works as a stabilizer and you won"t cut your carpet
I don't like the basting spray and this keeps everything in place.
Pin as usual, without going through the vinyl. Toss the vinyl that you don't need and save the big part left over.
Hope this can help someone.