This term comes from gambling in the American West where a wheeler-dealer was a heavy bettor on the roulette wheel and at cards. In time, it grew to mean to take part in clever but sometimes dishonest or immoral business deals.
Anyone who could “wheel and deal” in this way was certainly someone who could operate, manipulate and control situations for his or her own interest, especially in an aggressive or unscrupulous way.
By the 1940s, this colloquialism came to be mean the unsavory business dealings associated with perceived and actual big-time operators.