Norah,
I have a very large cutting table. In my former life I made draperies, bedspreads, etc., everything for the home when we lived in Washington, DC. It is 5' x 9' and is padded. My friends and I have basted many a quilt on this table since retiring. -- So to answer your question, it is stiff enough to hold the pins.
If the floor/rug is not an option for something large, perhaps you can consider using a mattress (one without a pillow top). Something you pin into and the pin holds without moving.
Hope this helps. Suzanne