Will the canvas drop cloths work?...yeah sort of ...most of them have a heavy seam down the center of a 15'x12', so watch out for how much is really useable area.

 

As far as backdrops you may be able to do some things easier than with hand painted drops.  For instance consider a silhouette of the NYC skyline to suggest NYC (don't forget to include the Chrylser Building and no twin towers!).  Not painted, just a true silhouette.   Then consider doing the mansion without walls-- just the stairs and two flower vases (massive) on either side and a nice chintz couch and chairs.  The flowers can be made of tissue paper.  The vases can be made from cardboard, styrofoam, etc.  Just paint them to look like China or cloisonne.  Want to really jazz up the mansion, project a stained glass window over the staircase. Or build one using a luan or cardboard frame and pieces of colored tissue paper glued on on wax paper.  Of you can make a sight joke by having a life size picture "frame" at the top of the stairs with Daddy Warbuck posed in it.  He 'enters' by stepping out of the frame and 'exits' by stepping back in.

 

For the orphanage: just bunk beds on wagons.  Use a gobo to project a desolate window behind them.

 

Your budget can be practically nothing if you suggest the settings and skip the walls.