Before the Wheel of Fortune became an American game show starring Pat Sajak and Vanna White, it was a medieval concept referring to a wheel spun by the goddess of Fate. The wheel would determine the fate of mortals. Nowadays, the Wheel of Fortune determines whether you win a brand-new car or a trip to Hawaii. The point is, spinning wheels are symbolically linked to destiny.
In the case of our protagonist, his attempt at spinning the wheel is not really about the jackpot money. It's about saving the woman he loves, Laura. Having the wheel stop at the correct number, therefore, is a matter of life or death for him, and once he begins pressing the wheel, he believes that he has control over life and death. He has control over the wheel and, thus, literally has control over fate. His refusal to make a decision may be interpreted as paralytic shock or as intoxication with the concept of having some measure of free will. Regardless, he has broken the rules of the bingo game by refusing to relinquish the button, and we may interpret the ending as a punishment.