Why are they doing it? The government says it wants more jobs, yet there is no area in American life with larger impediments between a willing employer and employee than labor.
I'm trying to bend over backwards to understand a worldview under which this is a sensible idea.
One possibility. Suppose this is your image of work: Take as given that a person has a job, and the employer will keep that job going, and won't change the terms of the job -- lower the base wage, allow people to take overtime, etc. Take as given that the terms of the job are a pure bilateral negotiation, and there is money somewhere to absorb extra costs without raising prices. Take as given also that the worker is in a bad negotiating position, and you, the benevolent central department of labor, care about moving this negotiation in the worker's way. Then, a rule like this is a way of strengthening the worker's bargaining position and driving some resources the worker's way out of the employer's pocket.
Here is an effort to put that debate in econ 101 supply and demand diagrams. Let's think of the rule as a mandated higher wage, like a minimum wage. The classic analysis says you get fewer jobs.
If that were the case, as you see, we wouldn't lose any jobs. There would be some unemployment, as more people want to work or employees want more hours than they can get. But I think advocates of these policies don't mind. Getting people to go out and look for jobs might not be so terrible.
Update: Good grief, Noah, of course "to understand the true impact of overtime rules, we probably have to include more complicated stuff!" Who ever said otherwise? Isn't "econ 101" clear enough that this is a an extremely simple starting place? And aren't you the guy complaining about excess mathiness, big black boxes in economics, and people who don't even try to understand the opposing arguments?