I saw an example of the recent popular fad cotton rug sewn with quilting cotton fabric and batting at my LQS. It was thin and lightweight. It seemed like a little strip quilt with a lot of top-stitching. I would be concerned with the type of thread more than the filler. It would need a good strong thread, in order to be durable and stand up to wear and use. But, I don't know if what I saw is what you intend to make. The one I saw seemed like the type of thing to use in the bathroom to step on when you come out of the shower, like a towel, something flexible, that is easily laundered.
About 15 years or so ago, there was a fad to wrap cotton clothesline rope with strips of fabric, and use that to create totes, baskets, rugs, etc. It might be more economical to use rope than batting, if you are interested to be conservative price wise (although I think that method would use more fabric). Rope would make a thicker, more substantial rug.
Along that idea-- using something other than batting-- you could use strips torn from an old sheet. I don't see why that wouldn't work okay to cover with fabric and sew together. I've used sheet strips for the inner layer in my rugs and it works great.
Just some ideas! Post some pictures of your rug when you have it complete! :-)