Tom Bombadil represents the only feasible alternative for dealing with the Ring. He's immune to its power. He can stand against just about anything Sauron could throw against him. He could keep the Ring. That means in the books, the Council of Elrond has a real choice to make. A terrible, difficult choice with consequences that could include the death of everyone in the room and all they care about if they choose incorrectly.

That's not really accurate though. In the books, Gandalf dismisses Bombadil as a possibility the instant Erestor brings it up. There is never any real "choice" presented. The option is suggested, and then immediately rejected.

"But Within those bounds nothing seems to dismay him," said Erestor. "Would he not take the Ring and keep it there, for ever harmless"?

"No", said Gandalf, "not willingly. He might do so, if all the free folk of the world begged him, but he would not understand the need. And if he were given the Ring, he would soon forget it, or most likely throw it away. Such things have no hold on his mind. He would be a most unsafe guardian; and that alone is answer enough."

-The Council of Elrond