Check this out:
“Let us first look at the American position, ably set forth and argued vigorously by General Marshall and his aides and by Harry Hopkins. We Americans had a straightforward view of the war in Europe. The way to beat Hitler was the shortest way - go across the Channel and engage his armies as close to Germany as possible. All resources, all effort should be put to that end. Any other use of those forces was a diversion and might jeopardize the Main Event. This was argued back and forth in the winter and spring of 1943.
The British were against this plan. They argued: (1) a cross- Channel invasion would be a very dangerous undertaking - as indeed it proved to be - and probably could not be mounted until 1944; (2) meanwhile the cream of the British and American armies was in Africa and must be used. We had promised Stalin continued pressure in 1943. What better way than to knock Italy out of the war and move up through the “Soft Underbelly”?
This of course was Churchill’s view. He saw also that this would protect the oil supplies and the other British and Empire interests in the Middle East. Both Hitter and Churchill regarded the Balkans as critical to success.”
http://www.winstonchurchill.org/i4a/pages/index.cfm?pageid=597
The Italian campaign received more support from Churchill during the war, and he was not happy when resources and troops were diverted for other campaigns.
Try “A Soldier’s Story” by Bradley. It is illuminating.