I'm reading a book right now that states the U.S. military needed to draft 5.8 million men, but could only draft 4.9 million from 1943 to 1944.
George C. Marshall also said, "I am sure people do not realize how close we cam to catastrophe. Shortages of personnel forced us to strip division after division that we had trained. This drove the division commanders to strenuous protests. Just as those new units were reaching an excellent standard of efficiency, we would rip them to pieces in order to provide men as replacements for the growing battle overseas. We lacked sufficient replacements because deliveries from Selective Service were short in terms of a hundred thousand or more. We were confronted with a terrible problem for which the armies in the field paid the price... We had just enough and no more, and it all went in."
Well, it's true that the US Army in particular suffered from manpower shortages late in the war, but:
they were nowhere near as acute as those suffered by the enemy, or their allies
Army personnel numbers did not peak until the very month Germany was defeated
they were not universal shortages
Basically the discrepancy comes out of what the military felt it needed, and what it actually got - by mid '43 the Axis was whipped and in the US all the 'excess' unemployed had been siphoned into the military or employed domestically; further mobilization was neglected in favour of maintaining strong domestic growth. To add to that lend-lease consistently hampered US military buildup, by depriving the military of armaments and making significant demands on industrial manpower which might have been employed elsewhere.
These shortages were made good by trimming the fat (cutting specialist training programmes, diverting more men from technical/support roles into combat roles, deploying the more frivolously-employed rear echelon personnel into rifle battalions), and expanding the roles of women and coloured men. The US took less casualties in Overlord and the following three months than it had reckoned for, and actually had surplus reserves - the problem was that the majority of casualties were incurred primarily in infantry units - the proportion of casualties estimated to be suffered by infantry units was consistently low, by around ten percent (around 68% of the total replacement pool in 1944, in practice it was approximately 77%). In effect, civilian planners asked the military to make do with what it had rather than to further expand mobilization when the end of the war was clearly in sight.
Here's a link to Army Ground Forces study #7 explaining the provision of replacements:
http://www.history.army.mil/books/agf/AGF007/index.htm#Contents
Mark Harrison's The Economics of World War II: Six Great Powers in International Comparison is a very good resource on the topic as well, you can read a good chunk of it on Google Books.
As a follow up, how close were the Soviets to exhausting their manpower?