See a clip from the interview at left or watch the whole thing here.
"Let me say this about members of Congress," Mr. Obama said during the taped interview. "Are you going to curse?" Stewart interrupted.
The president did not indulge, but the "Daily Show" host displayed less restraint in comments to the audience before and after taping.
Stewart, who described himself as "nervous" for the interview, said Mr. Obama sat down and gave him a look he read as "wanna go, mother f***er?"
Off camera, an audience member asked Stewart what he would have liked to ask Mr. Obama but wouldn't dare. "If my people control the media, then why am I still on basic cable?" (paraphrased) the Jewish Comedy Central star answered, referencing comments former.
In more Q & A, Stewart was asked who his favorite congressmen was. Though unable to answer because "there are so many good ones," Stewart did single out Rep. Barney Frank (D-Mass.) as the "cute one."
In a city full of pundits, Stewart called his job as a comedian "harder."
"Being a pundit you just have to open your pie hole," he said. "We don't fact check to be good journalists. We fact check because good comedy doesn't lie."
Stewart typically has a stack of papers on his news desk while on air, piquing a question from the audience. "Why do you have so many papers? You never even look at them."
The "Daily Show" host retaped the show's open to allow for more time for Mr. Obama's interview on air. It is not only the first time a sitting president has appeared on the show, but also the first time producers have dedicated the full half hour to one guest.
In the first take, which did not air on Comedy Central Wednesday, Stewart introduced Mr. Obama as the White House Council of Economic Advisers Chairman's boss. Austan Goolsbee was a guest on the "Daily Show" Monday.
Also not making air, a series Stewart called "Let's Make the President Wait," in which Stewart played with his pen and a paper football and ate M&Ms.
Without divulging any details of the program, Stewart encouraged the audience to attend Saturday's "Rally for Sanity," co-hosted by Comedy Central's Stephen Colbert.
"I don't know if we're going to bring it the way you want us to bring it,"
Stewart said, conceding, "You may just waste a few hours on the mall."
Stewart thanked the audience of about 500. "That's the show! That's why you stood out in the rain for nine hours with horse manure." The Verizon Center, next door to the Sidney Harman Center hosted the outdoor National Horse Show Wednesday.
Christine Delargy is an associate producer for CBSNews.com. You can read more of her posts here. For more of Washington Unplugged, follow us on Facebook and Twitter.