Boehner left the talks complaining the Democrats "will not negotiate".
Obama told CNBC before the meeting that he was "prepared to negotiate on anything" over the budget once Congress passes "a clean piece of legislation that reopens the government".
The US government closed non-essential operations on Tuesday
after Congress failed to strike a deal on a new budget.
The shutdown has left more than 700,000 employees on unpaid leave and closed national parks, tourist sites, government websites, office buildings, and more.
However, as one budget crisis raged in Washington DC, another one - potentially more dangerous - looms in the coming weeks.
On 17 October, the US government will run out of cash to pay its bills unless the debt ceiling is raised.
House Minority Leader Rep. Nancy Pelosi, D-Calif., left, with Senate Majority Leader Sen. Harry Reid, D-Nev., speaks to reporters following a meeting with President Barack Obama and the Republican leadership at the White House in Washington, Wednesday, Oct. 2, 2013.
he Ohio Clock outside the Senate Chamber on Capitol Hill shows the time of 12:01 a.m., in Washington. Having failed to persuade their traditional Republican allies in Congress to avert a government shutdown, business leaders fear bigger problems ahead.
People stand and jog, in front of the steps of the closed Lincoln Memorial, Tuesday, Oct. 1, 2013, in Washington. The museums that draw millions of visitors to the National Mall closed their doors Tuesday, memorials were barricaded and trash will go uncollected in the nation's most-visited national park due to the first government shutdown in 17 years.
President Barack Obama gestures as he speaks in the Rose Garden of the White House in Washington, Tuesday, Oct. 1, 2013, about the government shutdown. Congress plunged the nation into a partial government shutdown Tuesday as a protracted dispute over Obama's signature health care law reached a boiling point, forcing some 800,000 federal workers off the job.
President Barack Obama, accompanied by Health and Human Services Secretary Kathleen Sebelius, and people who support the Affordable Care Act, his signature health care law, speaks in the Rose Garden of the White House in Washington, Tuesday, Oct. 1, 2013.
The U.S. Capital is seen behind an area closed for restoration sign on the National Mall in Washington, Tuesday, Oct. 1, 2013.
The left side of the table from right Secretary of Agriculture Tom Vilsack, Secretary of Treasury Jack Lew, Vice President Joe Biden, Attorney General Eric Holder, and seated on the right side of the table from left starting with Secretary of Environmental Protection Agency Gina McCarthy.