" .. the payroll withholding system he developed (while he was still a Keynesian) ..."
I think it was Albert G. Hart, then a professor of economics at Iowa State, who first put forward what subsequently became the 1943 withholding law. Hart's testimony before Congress was in January 1941, before Friedman started working at Treasury. Friedman was on the Treasury's tax-research staff which evaluated various withholding proposals, including Hart's. I remember reading an interview with Friedman (in Reason magazine, I recall) in which he defended withholding as an emergency wartime measure, but regretted that it was not repealed after the war.
The definitive study on withholding here. Print for your permanent records...
http://www.cato.org/pubs/journal/cj14n3-1.html
EVOLUTION OF FEDERAL INCOME TAX WITHHOLDING: THE MACHINERY OF INSTITUTIONAL CHANGE
Charlotte Twight