She proposed the idea to congressional spouses on Thursday during their annual first lady's luncheon.
Since moving to the White House, Mrs. Obama has promoted the issue by volunteering herself.
On Wednesday, she and Jill Biden, the vice president's wife, and more than 100 congressional spouses spent the afternoon at a food bank bagging lunches for hungry children. She also has helped serve meals at a soup kitchen and assemble care packages for U.S. troops.
The annual Congressional Picnic is scheduled for June 25. The event provides a relaxed environment where lawmakers, the president and administration officials can set aside their policy differences and socialize over food and music on the South Lawn.
"We can bring our husbands and our wives, our children and our grandchildren together as we did yesterday and rally around a common cause," Mrs. Obama said during her luncheon speech at a hotel. "This would be a powerful message that we could send to people around the country, that they saw all of our families come together here in D.C."
Thursday's luncheon was closed to the media, but the White House released a transcript of the speech.
In the remarks, Mrs. Obama also shed a little more light on her new White House life.
Daughters Malia, 10, and Sasha, 7, are happy and getting good grades at their new school.
There's soccer on Saturdays -- "Yes, I'm on a soccer field all day, just like many of you," she said -- and slumber parties, including one recently with seven "screaming and yelling" girls.
"And we're shuttling kids back and forth to play dates, just like usual, although now my mom does a little more of the shuttling than I do," she said. "I'm glad to have her here."
Mrs. Obama's mother, Marian Robinson, 71, moved with the family from Chicago to help care for her grandkids.
"She has a very full social life, so much so that sometimes we have to plan our schedule around her schedule," Mrs. Obama said.
The first lady already has eaten salad made with greens from the garden she planted on the South Lawn. She also offered some advice to congressional spouses whose kids are begging for a dog, as her own daughters did.
Bo, a Portuguese water dog, joined the family about two weeks ago.
"Even though the kids are supposed to do a lot of the work, I'm still up at 5:15 a.m. taking my dog out," Mrs. Obama said. "So for everyone who has a child asking for a puppy, you have to want the dog. As I do. I love my Bo."