Walker, who has spent the past couple of years advising lawmakers on both sides of the aisle on crafting a solution to the nation's soaring debt, said now is not the time for "grand bargains" and stubborn politics.

Instead, he said, they should heed the lessons of past efforts. That means steering clear of airing differences in public to avoid bruising egos or igniting tempers.

"You need things to be more private when you're trying to deal with the key decision makers," Walker said. "They have to save face. They are human after all."