"I wouldn't want anybody but Barack Obama to be working at this time, because he is a focused, clear-thinking, rational man -- and that's what we need right now," she said. "I'm coming off of a boost of understanding all that our country is made of, the values, the men, the women, people who are looking for the silver lining, even in tough times."
The first lady told Roberts about how she has taken time in the first few weeks in the White House to get to know the new city she now calls home and to make the rounds visiting various federal agencies. She has met with thousands of men and women who now work for her husband.
She makes these visits to thank the people she calls "the backbone of our government," and rally them for more work ahead.
It's also a chance for her to hear the concerns of federal government employees and relay them back to the president.
At each stop, she makes a point to meet privately with a smaller group of staffers before she delivers remarks. She has asked to meet with the longest-serving staff members at these agencies, and when she visited the Department of Interior last month, some of the employees she spoke with had worked there for nearly 40 years.
"Part of what I want to do is to tell them, 'Thank you. Thank you for your service.' They make up the foundation of this democracy as well," she said.
She plans to get to every federal agency over the next few months.
Michelle Obama is adjusting to her many new roles, including hostess-in-chief, she said. The first family has hosted regular Wednesday night social gatherings at the White House and two formal dinners in less than two months.
For Super Bowl Sunday, the Obamas opened the White House to friends and members of Congress and their families.
Living in a home with antiques, historic artifacts and two small children might be an accident waiting to happen, but the first lady said, so far, the children have not broken anything.
"We've had some guests who've broken some things but not the kids," she said with a laugh. "And they know who they are."
Both the first lady and the president have talked about the simple joy of being able to eat dinner together every night at the White House after two long years on the campaign trail.
"There's time to breathe a little bit, at least as a family. We're breathing in a way that we haven't breathed in a long time. And it feels good," she told Roberts.
Her daughters, she said, are doing "great" after two months in Washington.
"I think they're doing great because I've been able to strike a balance," she said. "I have a pretty full plate, but I still have time to be home for homework and to make sure I'm there before they leave, and to go to their parent-teacher conferences and all the things that it's important to do as a parent. So they're doing great. They keep us going."
The first lady credited her mother, Marian Robinson, with helping to ease the transition for her and her daughters and called Robinson's presence in the White House "immeasurable."
"First of all, she's one of the funniest people I know. And she's so nonimpressed by any of this. She keeps all of our feet on the ground," Michelle Obama said.
Robinson is there to lend a hand with the girls when the first lady's own schedule prevents her from being there, she said.