I am sure lots of elk are killed every year with a 270. However, I suggest a quality 150gr premium bullet if you must use the 270. I rifle hunt (guided) in NM every year and the outfitter won't let his hunters use anything smaller than a 7mag. Said he got tired of chasing wounded animals all over the mountains or losing them. As with any hunting, it's the shot placement and bullet construction that bring home the bacon. For me, I use a 300 WSM with 180gr Nosler Partitions, but if you feel confident you can place a good 150 gr bullet in the vitals, go for it.
Good Hunting,
Hal