What are some cheap ideas to smoothen the surface of a papier mache?
I've used setting joint compound, it has common set times of 20, 45 and 90 min.  You mix it with water to any consistency you'd like.  The setting mud will let you do 2-3 coats per day.  



You might need to reinforce the first paper-joint compound layer by using mesh tape.  The tape  will let the mud hold to it and will stiffen the sculpture, so it won't flex and crack off. Resist sanding until no paper or tape shows through.  The self adhesive (of the tape) is not superstrong, so you may need to tack it down with craft glue is areas where it bends.  Once overcoated with mud, it will behave.



It can be overlapped as needed, troweling the mud over it will squeeze through and lock down.