For President Reagan, to be fair, we should note that his early years were hurt by the same force that crushed payrolls under President Carter during April through July of 1980: the high rates with which Paul Volcker battled inflation. Double-digit prime interest rates diminished employment under both Presidents Reagan and Carter. While those unusually high interest rates may have been necessary to get control over inflation, those high rates severely slowed expansion and thus hiring. However, that doesn't remove the possibility that President Reagan's descent from Carter's payroll numbers hinted at the start of a Republican trend under Trickle-down policies. After all, the Bush I policies were largely a continuation of the Reagan policies. If we average together the Reagan and Bush I months, together they get 113.3 thousand jobs / month. That's less than either of Carter or Clinton. And it's also less than the rate of increase we've seen since the turn-around on 2/1/2010 under President Obama.
While these figures aren't conclusive proof alone, add them together with a few other factors such as that GDP growth has lagged under the lowest top marginal tax rates. It sure looks like Trickle-down (or Supply-side economic or Reaganomics) failed us in a big way.
Maybe we should stop accepting the notion that talking about lowering taxes and deregulating would actually be business-friendly. Maybe we should instead consider ways to return to the sort of sensible, progressive tax structures we had before Reagan lead us down the road to decline. Instead of calling it red tape, maybe we should consider regulation's value for helping business manage risk, compete on a level playing field, and have more predictable returns. And maybe we should get back to expecting serious infrastructure projects and demanding aggressive investments in our research and development programs to build our avenues for growth.
Notes on methodology: Generally speaking, the January in which the executive transitions from one branch to another will be almost entirely impacted by the outgoing President's policies and not those of the incoming President. As such, the average uses the change in monthly manufacturing payrolls starting with the change from the first full month of the President's term (i.e., from the February that is the first full month to the March thereafter) and going until the first full month after the President's term (i.e., the last change counted is from the January during which the President in question is last in office to the February thereafter). Data from BLS/FRED.