It will throw off the speedo by some few miles per hour depending on how big or small from stock it is. It shouldn't keep it from working, though. Check the cable at the transmission where it screws in. It's either screwed in or bolted in with a 10mm bolt. Once you remove it from there you should see if there is damage or wear at the little gear thats there. It's made of plastic so if its never been replaced it may be as old as the car. It happens some times. I go to a web site hosted by mazda miata folks to compare tire sizes and such. On the search bar I type "tirecalc" and the first link to pop up is their site. It helps a lot when upgrading to bigger tires and wheels. Checkem' out.  

Ok thanks again black monkey i will check it out and let you know whats up with it. thanks for the web site.