Absolutely coyotes will have a bad effect on the deer population. Here in Washington I've seen them after even adult mule deer, and the fawns are easy prey. In the winter, adult mulies can become prey.
Coyote size likely has something to do with it. We get some big ones here - I shot one a few years back that measures a full 60" from tip of nose to tip of tail. Kept that hide, but have seen others of equal size since. He probably weighed close to 50 pounds too.
I didn't take the attached photo - borrowed it from another web site where it caught my attention. The story said that it was two 'yotes going after a mature mulie buck near Yellowstone National Park. From what I've seen, I have no trouble believing it. Just this afternoon I took a shot at a yote at about 350 yards. Have to admit that I missed him, but I'll be back out, after them again all winter long while the mulies are most vulnerable.