Obama was interviewed for the show four times before he was elected commander-in-chief in 2008, however.
Wednesday's appearance was scheduled during the series' week-long trip to Washington to provide viewers with "Indecision 2010" coverage of the midterm elections, Comedy Central said.
Show producers said this is the first time an episode has consisted of a single guest interview.
"Are we the people we were waiting for, or does it turn out those people are still out there -- and we don't have their number?" Stewart queried the president.
"I am feeling great about where the American people are, considering what we have gone through," Obama replied. "We have gone through two of the toughest years of any time since the Great Depression ... . There is still a lot of good stuff happening, but people are frustrated."
He went on to say "the economy is growing," but not as strong as it needs to and pointed out how he prevented a second Great Depression, stabilized the economy, passed historic health care reform and financial reform during his tenure at the White House thus far.
"We have done things that people don't even know about," Obama said.
"What have you done that people don't know about? Are you planning a surprise party for us?" Stewart joked.
Obama reiterated his accomplishments and admitted: "Is it enough? No."
"So I expect and I think most Democrats out there want to see more progress," the president added. "We have done an awful lot that we talked about in the campaign and we are going to do more."