you could see anything from mid 50's to high 70's during the day..in mid march i bring a few pairs of shorts cause if its in the 70's i want to be comfortable walking the strip I would suggest planning for an average high of 70
Some of it depends on what you classify as "shorts weather" We've been to Vegas when it would be classified as definitely shorts weather back home and while my wife and I were out and about in shorts and t-shirts during the day there were still lots of people bundled up heavy winter coats that looked like they were freezing.
Averages for March 15th are a high of 70 and low of 49. Anything over 65 is warm walking around in the sun, but cool in the shade. Expect it to be chilly after the sun goes down. It seems like I'm always there in March and as mentioned before, I've seen it not get out of the 50's and I've seen it in the 80's.
It can very dramatically over a few days. When I first arrived on a March trip, it was quite cold and windy, but 4 days later it was very balmy. I'll mix in some jeans and shorts, with one sweatshirt and a light jacket for nights.
Today (half Feb) it's already 55F/13C. In March it's maybe around 68F/20C during the day, but at night it still can get quite chilly, less than 45F/7C.