In the run-up to Donald Trump's inauguration next week, we have seen two Georgia Democrats of legendary stature hold out olive branches to the incoming Republican administration.

This morning, former U.S. senator Sam Nunn vouched for Exxon Mobil CEO Rex Tillerson as Trump's choice for secretary of state.

“I consider Rex Tillerson’s experience and knowledge in business as an asset – not a liability,” Nunn said.

Then there is former President Jimmy Carter, who, following Trump’s victory, was the first ex-resident of the White House to say that he would attend next week’s inauguration. Even as George W. Bush and Bill Clinton held back.

Both Carter and Nunn have reasons to repair some singed bridges. In late October, in a Wall Street Journal op-ed piece, Nunn – who backed Hillary Clinton – described Trump "as an apprentice in the nuclear arena" who had "no appetite for learning."

Early last year, Carter damned Trump with faint praise, telling the British Parliament that he'd rather see Trump in the White House rather than Republican rival Ted Cruz. "Trump has proven already that he's completely malleable. I don't think he has any fixed opinions that he would really go to the White House and fight for," Carter said last February.

If you asked either Georgian today, you would probably be told that moving on and accepting election results is a major part of our civic duty. And both Nunn and Carter would be quite sincere about that.

But both men are also still building post-political legacies that could depend, in large part, on a successful Trump administration – and on maintaining good relations with that administration.

Tillerson has also been a fierce backer of maintaining U.S.-Russia relations, a position that's prompted criticism from Democrats and many Republicans. Nunn and Tillerson served together on the board of trustees of the Washington, D.C.-based Center for Strategic and International Studies.

Then there's Carter, who was at the presidential library in Atlanta this morning talk about the opening of a new exhibit, "Countdown to Zero," about the world's efforts to eradicate a number of diseases, including Guinea worm disease.

The Carter Center has worked with governments, health agencies and nonprofits across the world to eradicate Guinea worm disease.

That includes the U.S. government, which the former president was forthright about. Said Carter:

"Of course, we are dependent, in some cases, on U.S. AID. I'll be going to the inauguration. I'll be meeting with President-elect Trump, and also with the new secretary of state, who has charge of U.S. AID, to let them know what we're doing."