Dulles shakes Zhou Enlai's hand at Geneva, 1954

One famous anecdote from the Cold War is the one about Secretary of State John Foster Dulles rejecting the offered hand of Zhou Enlai to shake at the Indochina peace talks in 1954. What would have happened if Dulles and Zhou actually shook hands in public, out of politeness? How would this affect Sino-American relations? How about the political and public reaction in the States? Would Dulles get the pink slip from Ike?
 
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