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
More on Ruml. The germ of the withholding idea appears to be his.
http://www.amityshlaes.com/articles/1999/1999-04-15.php
“But even in this most patriotic of moments, it was not evident that Americans were willing to pay the new tax. In those days, taxpayers sent one big check to the government. And as spring arrived in 1943, it appeared that many citizens might not ante up and file returns. Henry Morgenthau, the Treasury secretary, confronted colleagues about the nightmarish prospect of mass tax evasion: “Suppose we have to go out and arrest five million people?”
Enter Ruml, man of ideas. Like other retailers, he had observed that customers didn’t like big bills. They preferred installment payments, even if they had to pay interest to relieve their pain. So Ruml devised a plan, which he unfolded to his colleagues at the Fed and to anyone who would listen in Washington. The government would get business to do its work, collecting taxes for it. Employers would retain a percentage of taxes from workers every week and forward the money directly to Washington’s war chest. No longer would the worker ever have to look his tax bill square in the eye. He need never even see the money he was forgoing. Thus withholding as we know it today was born.
To tame resistance to the new notion, Ruml offered a powerful sweetener: The federal government would offer a tax amnesty for the previous year. It was the most ambitious bait-and-switch plan in America’s history.
Ruml advertised his project as a humane effort to smooth life in the disruption of the war. He noted that it was a way to help taxpayers out of the habit of carrying income tax debt, debt he characterized as “a pernicious fungus permeating the structure of things.”
Ruml’s genius did not lie in inventing withholding, already a known, if largely untried, tax concept. His genius lay in packaging so clever it provoked envy from his peers. Randolph Paul, a tax authority at Treasury, wrote distastefully that Ruml seemed to have convinced taxpayers he had found “a very white rabbit”-a magic trick-”which would somehow lighten their tax load.” Ruml called his program not “collection at source” or “withholding,” two technical terms that might put voters off, but “pay as you go,” a zippier name. Most important of all was the lure of the tax amnesty.