1949, American English, apparently coined from V.P., abbreviation of vice president, perhaps modeled on jeep, which was then in vogue. Introduced by Alben W. Barkley (1877-1956), Harry Truman's vice president. According to the "Saturday Evening Post," "his grandchildren, finding Vice-President too long, call him that." The magazines quickly picked it up, especially when the 71-year-old Barkley married a 38-year-old widow (dubbed the Veepess).
Barkley says word "Veep" is not copyrighted, and any vice president who wants to can use it. But he hopes not many will. [U.S. Department of State wireless bulletin, 1949]
"Time," tongue in cheek, suggested the president should be Peep, the Secretary of State Steep, and the Secretary of Labor Sleep.