Former Obama aide Jen Psaki said that the president has learned during his time in office.

"The president is a pragmatist, and he wants to get things done," she said. "And he knows that compromise is a part of that. And that's how he's been able to move many things forward. But there's no question that he's learned. He has learned that having the will of the American people behind you and working directly with them is more important than having a conversation within the cauldron of Washington."

Hess argued that the president will have built a significant legacy if he is able simply to oversee the implementation of the health care law passed in his first term.

"He passed that, but it's got a lot of rough edges," he said. "If only in the next four years, he got that into working shape so that when he left the White House, he left that behind, that's a pretty major step forward. It's up there with Social Security and Medicare. So in some ways that's the most important."

Hudak said the president can't let the perfect be the enemy of the good.

"He has to set aside what he would love to do for what he can do," he said. "And if he focuses on what he can do, he'll have a hell of a list of legislative accomplishments in his second term. But if he focuses on the ideal, he'll have a 'second term curse' in terms of policy."

Duberstein agreed, saying that "there's a tendency sometimes to overreach or to have too many priorities or too many initiatives rather than order the two, three, four items that I want to get done in my second term." Brinkley, meanwhile, argued that the second term is the time for big, dramatic action.

"People want something bold, something memorable," he said. "They want to know, 'Where is he leading us? What's the 'moon shot' of our time?'"