Stewart, a House freshman, said he appreciated that the president reached out to Republicans and said one positive outcome is "the door is now open."
Rep. Jason Chaffetz, R-Utah, has been in these meetings before, the last one taking place in 2011. He said the real benefit would come from more regular interactions with the president and his top advisers.
"I give him huge credit for having the dialogue. I just wish we would do this more often," he said.
None of Utah's three Republican members asked the president a question during the afternoon meeting in the Capitol's basement. Rep. Rob Bishop, R-Utah, was not immediately available to comment on the discussion.
The president told Republicans that his forthcoming budget would not balance in the next 10 years and that he doesn't think that is a top priority. Obama made the same point in an interview with ABC News this week.
"We've got some big disagreements on the budget. But we've made some big cuts," Obama said. "There's not, in any way, an immediate crisis with respect to our finances."
He added: "My goal is not to chase a balanced budget just for the sake of balance. My goal is how do we grow the economy, put people back to work, and if we do that we're going to be bringing in more revenue."
Chaffetz said hearing the president make a similar point at the Capitol on Wednesday was stunning.
"That is so polar opposite from my vantage point and thinking," he said."To hear him say it out loud, that was the part that stuck out to me more than anything else."
Republicans also took issue with the White House's decision to cancel tours to save $3.7 million per year in Secret Service costs as part of the budget sequestration. Stewart calls it a symbolically important move that shows that the public must make a sacrifice, when the president could have saved the money through other means.
Stewart introduced a resolution Wednesday urging the president to cut out his annual family trip to Hawaii, where he was born, because it costs the government about $4 million.
Obama deflected the criticism, saying the decision didn't reach his desk and was made by the Secret Service, a comment that caused some GOP members to audibly groan.
The president told ABC News that he's asked the Secret Service for a way to allow school groups to tour the White House, and he took a shot at the GOP contempt for the decision.
"I'm always amused when people on the one hand say the sequester doesn't mean anything and the administration's exaggerating its effects; and then whatever the specific effects are, they yell and scream and say, 'Why are you doing that?' " Obama said. "Well, there are consequences to Congress not having come up with a more sensible way to reduce the deficit."
The president will meet privately with Senate Republicans on Thursday.