Any change of the rules by majority will set the precedent.
Reid has 30 or 40 members who really want this, newer members and members who came up through the House, or are deeply indebted to special interest groups- or to Obama’s machine.
He’s got about a dozen who don’t want to lose the power the present system gives individuals or don’t want to tarnish their ‘moderate’ ‘bipartisan’ patina.
I don’t think he can do it, or can afford to. Though it would give him more power personally.
The Senate rules have been changed by a simple majority, but that was early in the history of Congress; like about 10-15 years in. The "unlimited debate" paradigm came about when the motion to call the question was eliminated in, IIRC, 1804. That rule change was adopted by a simple majority.
The Senate is a truly dysfunctional body. Congress has run the country into the ground. There isn't enough shame and opprobrium in the universe to give Congress the legacy it has earned itself.
I quit watching the Senate close, about 4 years ago. I suspect you are correct that he doesn't have a simple majority to go along with his plan to toxify the body.