First of all, is he talking about short run or long run aggregate supply?
Well, I just spent like...20-30 minutes looking for and through my notes.
They (the notes) didn't really specify, but according to my book:
"To summarize: Lower marginal tax rates encourage saving and investing. Workers therefore find themselves equipped with more and technologically superior machinery and equipment. Labor productivity rises, and that expands long-run aggregate supply and economic growth, which in turn keeps unemployment rates and inflation low." So it looks like long run.
Also, "Supply-side advocates respond to the skeptics by contending that the Reagan tax cuts in the 1980s works as Laffer predicted."
I also remember another one of the counter arguments.
This time regarding the Phillips Curve.
The economics text I have agrees with you...sort of.
It says that in the short run
that unemployment and inflation are inversely proportional (decrease one and you increase the other), but that this relation disappears in the long run
(called the Long Run Phillips curve).