When someone doubles over from stomach pain, the general surgeon is the one who performs an appendectomy. Gallstones? The general surgeon removes the gallbladder. Breast and colon tumors and hernias are also matters for the surgeon's scalpel.

Now the economic and cultural forces reshaping U.S. medicine are prompting an exodus from this once venerable field, creating a growing market for temporary surgeons-for-hire.

As...