He helped design it in 1942. He decades later said he favored its abolition.
Beardsly Ruml is generally given greater credit for the concept of withholding.
http://www.bloomberg.com/news/2012-02-23/the-founding-father-of-modern-income-taxes-echoes.html
“Enter Ruml. The treasurer of R. H. Macy & Co. and chairman of the Federal Reserve Bank of New York, he advanced the idea of having taxpayers make installment payments during the year, either directly or at work. This would relieve them of having to pay the whole amount at year’s end and regularize the flow of revenue to the government.”
Friedman did acknowledge his role in the plan.
http://reason.com/archives/1995/06/01/best-of-both-worlds
“Reason: You were involved in the development of the withholding tax when you were doing tax work for the government in 1941-43?
Friedman: I was an employee at the Treasury Department. We were in a wartime situation. How do you raise the enormous amount of taxes you need for wartime? We were all in favor of cutting inflation. I wasn’t as sophisticated about how to do it then as I would be now, but there’s no doubt that one of the ways to avoid inflation was to finance as large a fraction of current spending with tax money as possible.
In World War I, a very small fraction of the total war expenditure was financed by taxes, so we had a doubling of prices during the war and after the war. At the outbreak of World War II, the Treasury was determined not to make the same mistake again.
You could not do that during wartime or peacetime without withholding. And so people at the Treasury tax research department, where I was working, investigated various methods of withholding. I was one of the small technical group that worked on developing it.
One of the major opponents of the idea was the IRS. Because every organization knows that the only way you can do anything is the way they’ve always been doing it. This was something new, and they kept telling us how impossible it was. It was a very interesting and very challenging intellectual task. I played a significant role, no question about it, in introducing withholding. I think it’s a great mistake for peacetime, but in 1941-43, all of us were concentrating on the war.
I have no apologies for it, but I really wish we hadn’t found it necessary and I wish there were some way of abolishing withholding now.”
It was actually codified in law by this act.
http://www.taxhistory.com/1943.html