I had read this idea somewhere but finally got around to trying it. It works great!
To make an easy, cheap, effective base for purses, buy a square floor tile (I guess it's linoleum) and cut it to size. These are the peel and stick kind...mine is 12" square and cost about 70 cents at Home Depot. I used a pencil and one of my quilt rulers to mark the tile to size, then used the ruler and a utility knife to cut it (after several slices I could bend the tile back and then cut through the paper backing).
It provides just the right amount of flexibility and support. You can, of course, make a fabric envelope for it (I refer not to sew mine closed, so that it can be removed when the purse and base cover are washed).