One problem I see is using a vinyl roller shade. I'm afraid the temp at which you would apply iron-on interfacing would melt the vinyl. Do they still make paper shades?

I've done this with fabric and interfacing without problems. It depends on your fashion fabric weight; you might not even need anything at all, really. If you want to strengthen your fabric, use any comparable adhesive/iron on interfacing -- not too heavy -- it has to roll up, remember. You don't say how wide your window shade will be; it doesn't really matter, just be sure you follow manufacture instructions adhering the backing to the fabric. Toss the vinyl; you could have purchased the roll-up rod without a shade and they probably would have cut it to length for you. Be sure to attach your fabric/backing with sturdy staples onto the roll-up rod (maybe there's something else to use these days -- but secure it properly, making sure the roll-up is going in the right direction; put the shade into the sockets and you will be just fine! If you made a pocket for the bottom of the shade you can insert a wood piece or a dowel or a decorative pull. I hope I helped some.
Annie

Did you google on line under "how to make a roller shade"? I found some sites like HGTV and DIY that have lots of ideas. They use spray adhesive to attach fabric to the shade.

Thanks all! Sorry, I should have clarified -- I was thinking of ditching the vinyl part altogether. I just want to use my fabric with some sort of iron-on interfacing or stabilizer. I'm kinda handy but sewing is not my thing, thus my question.

It is my understanding you need a shade of some type to attach the fabric to. I've never seen one made with anything but a shade for stabilizing.

This can be done. I made a pair a long time ago for my now 11-year-old's nursery...so I couldn't tell you exactly what kind of interfacing I used...BUT. I used the original vinyl shades that were on the window for the mechanisms (old-fashioned and inexpensive spring-style which I presume is what you're going to use) Removed the vinyl shades altogether...and used them as my pattern as far as length and size of the pocket to slip the mechanism back through. I fused interfacing to my fabric first, then did all the cutting and sewing of this new heavier, stiffer fabric. It was still relatively thin because I used a cotton print and not decorator fabric. They worked just fine for many years. Try it out with some remnant fabric first to get your construction correct...and yes, you'll have to pay attention to the direction you wrap the fabric around the mechanism in order to get it to work correctly. Good luck!

I used pure fabric, no interfacing, and tossed the vinyl. If the fabric's the right weight (mine is a fairly dense cotton/linen blend) you won't have any problems.
The tough part is deciding how to hem your sides - you could use stitch witchery (2-sided fusing), sew it down, or just leave it, making sure you've cut it exactly along a thread (this is what I did since the linen is pretty stable). I sewed the plastic weight from the vinyl shades into the bottom.