Reid and Boehner will meet with Obama again today, for the third time this week, to hash out a deal.
Today's rhetoric is markedly different than the tone of optimism that was struck after Wednesday night's meeting.
"I thought the meetings were frank, they were constructive and what they did was narrow the issues and clarify the issues that are still outstanding," Obama said Wednesday night.
Boehner also cited "progress," but suggested "some honest differences" still divided the two parties' negotiating teams.
"I want to reiterate that there is no agreement on a [dollar] number and there no agreement on the policy," Boehner said. "But there's an intent on both sides to continue to work together to try to resolve this. No one wants the government to shut down. We are going to continue to work throughout the night and tomorrow."
Obama suggested he would keep the pressure on both sides.
"We're going to keep on pounding away at this thing because I'm absolutely convinced that we can get this done," he said. "There is no reason we should not be able to complete a deal."
Obama cited the real-life story of J.T. Henderson, which was reported by ABC News. Henderson is expecting to receive a large tax refund to pay bills.
"A shutdown could have real consequences for real people," Obama said. "There are ramifications all across this economy, and at a time when the economy is still coming out of an extraordinarily deep recession it would be inexcusable, given the relatively narrow differences when it comes to numbers between the two parties, that we can't get this done."
If a deal to fund the government cannot be reached, at least 800,000 federal employees are expected to be furloughed, the same as during the 1995 government shutdown. But unlike then, it's unclear whether they would receive back pay for the lost time.
Troops and other agency staff that are considered "essential" and kept on duty during a shutdown will not receive paychecks until Congress makes a deal.
Members of Congress, however, will continue to be paid. Every lawmaker must decide which of their employees is considered essential and should be kept on staff while the government is shut.
The clock quickly is running out for lawmakers. Current funding expires at midnight on Friday and a House bill needs to be presented 48 hours before it is brought to the floor for a vote.
Democrats blame Boehner for caving in to Tea Party pressure and backing away from the $33 billion in cuts they say they originally negotiated with him. Boehner has said the two sides never agreed to that number.
In an interview with ABC News' George Stephanopoulos, Boehner said he is in full agreement with conservative Republicans affiliated with the Tea Party.
"What they want is they want us to cut spending," Boehner said. "They want us to deal with this crushing debt that's going to crush the future for our kids and grandkids. There's no daylight there" -- between Boehner's position and the Tea Party's position.
Tea Party-backed members of Congress want to stick to the $61 billion in cuts proposed in the original continuing resolution that passed on Feb. 19. The two short-term extensions that the House has passed in recent weeks cut a total of $10 billion.