How low of a budget. The cardboard is not a really bad idea. The hard part is collecting enough of it to make a worthwhile maze. Next hard part is getting rid of it after you are done. If you collect the boxes and stack them just right and locked them together somehow, you could come up with a doable maze building material.
Picking up a few boxes each day is a good way to get them. Supermarkets are good (as suggested above). Another source that a lot of people overlook are fast food places. I worked at a chicken place and they threw out 20 or so boxes a day. Most areas have a few fast food places. Get in with them and you can build a pretty good supply fast.
You might be able to use warning barrier to make a maze.
A hundred feet of the stuff is about $25. You would need a lot of posts to make it work though. That is where the expensive part comes. Lets that you want a 20X20 grid. That is not too large of a maze but it is decent size for some fun. You would need over 400 posts to make it work. At a couple of dollars a post plus the code of the fencing it would easily cost you over a thousand to make it. So that probably is a no go. Still, if you can find a way to get enough posts cheaply then that grid stuff would work well.
Another idea is to use bales of hay. You run into the same problem of money though. They are a few dollars apiece. You would need hundreds of them to do the job.