We don't know what the two rivals discussed, but here are three challenges that we hope came up.
(The Root) -- Just before the election, I wrote a column for The Root: "The 9 Debate Questions We Want to Hear ." The eighth question on the list was this:
If, on election night, your opponent offered to meet with you on a regular basis in a spirit of bipartisanship to discuss ideas for moving the country forward -- the way many ex-presidents work together in solving issues across party lines -- would you be willing to do it, regardless of which one of you wins?
The premise was that these were questions we all wanted answered but knew that we would never hear asked at a debate, let alone answered. But in his election-night victory speech, President Obama did what he has done throughout much of his political career: surprised people. He said,  "From George to Lenore to their son Mitt, the Romney family has chosen to give back to America through public service and that is the legacy that we honor and applaud tonight ... In the weeks ahead, I also look forward to sitting down with Gov. Romney to talk about where we can work together to move this country forward."
And Thursday Gov. Romney did something surprising, too: He actually took the president up on his offer, joining him at the White House for an hour of conversation over turkey chili. In my previous post, I concluded:
Candidates pay a lot of lip service to things like "bipartisanship," but that's talk. You learn by watching what people do. For instance, John McCain (R-Ariz.) was one of the Senate's greatest champions of bipartisanship, until he lost to someone he didn't really like. But if Romney or Obama committed to working together in some way, regardless of who wins, that would tell us more about their commitment to bipartisanship than their speeches.
Though no one is expecting the two men to leave lunch as BFFs, the fact that they agreed to meet at all speaks volumes about their characters. Most presidential rivals don't engage this way.
So below is a list of the topics that, in an ideal world, the two men will have covered in their lunch, even if it is unlikely that they did. But just as we learned from my previous column, we can always hope that they will surprise us.
1. What can we both do to help heal the racial divide?
According to studies , race relations have actually become more strained since President Obama became commander in chief instead of better, as many had hoped and assumed they would. But as I have previously written, I believe in the long term that the Obama presidency, particularly his re-election, will prove a boost to race relations. But the president can't do it alone. Though GQ magazine  recently named Romney one of the country's least influential people, millions of Americans did pull the lever (or fill in a bubble) for him at the voting booth, and Romney could help lead them by example.
For instance, there were hundreds of racist tweets written by Romney supporters in the wake of the president's re-election. Just think of how effective it would be if Romney said, "I may not agree with President Obama on every issue, but I never agree with racism or racist comments in any context, including those directed at our president. I expect more from my fellow conservatives."
2. How can we both help tackle poverty?
In case you haven't heard, Obama and Romney have a difference of opinion on taxes , specifically whether or not wealthy Americans should pay more of them. But according to both men, they care about helping the poor. While Romney will never become an advocate for the president's efforts to raise taxes on wealthier Americans to fund services for poorer Americans, they could find common ground on securing more commitments from the country's wealthiest Americans for charitable efforts that aid the poor.
The idea is not as far-fetched as it may seem. Recently a group of billionaires, including Oprah Winfrey and Bill Gates, met to discuss how to use their fortunes in the most philanthropically generous yet strategic way. Imagine if the former governor convened a group of his wealthiest donors for a similar discussion. Think of it this way: There are wealthy Americans who may not want to see their tax dollars support FEMA because they consider it to be incompetent, but they might write a hefty check to the American Red Cross or another, similar private organization to do similar work.
It is worth noting that New York Mayor Michael Bloomberg tapped wealthy heiress Caroline Kennedy to run a nonprofit aimed specifically at raising private funds for the city's public schools. Kennedy's connections took the Fund for Public Schools from around $3 million to more than $200 million in its coffers. Romney could play a similar role at a national level, if he is willing to do so.
3. How can we both help end partisan gridlock?
One of the most common criticisms of the Obama presidency is that he has not "reached across the aisle" and displayed the spirit of bipartisanship that he promised on the campaign trail. However, the president has had little help on this. According to various accounts, Republican senators -- even those who were willing to work with the Obama administration on various issues -- were warned by Republican leaders not to do so.
Though Romney is not exactly a darling of the conservative movement, if he lent his voice to championing moderate candidates -- like the one he was as governor of Massachusetts -- over Tea Party extremists, and criticized both parties honestly when they engaged in behavior and rhetoric that undermined bipartisanship, he could be remembered for having more of an impact outside of the White House than he would have had inside.