WASHINGTON — A visibly frustrated President Obama emerged from a failed meeting on a budget deal Tuesday and said he would demand daily sessions with House Speaker John Boehner until an agreement was reached to prevent a U.S. government shutdown at week’s end.

Obama spoke not long after Boehner’s office issued a statement that insisted the two sides remained far apart and that Republicans had never, as the White House contends, agreed on $33 billion in cuts to the federal spending allotment for the remaining six months of the fiscal year that ends Sept. 30.

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President Obama said Tuesday he would demand daily meetings with House Speaker John Boehner in an attempt to reach a budget deal and avoid a government shutdown. The Associated Press

Obama, Vice President Joe Biden, Boehner and Sen. Majority Leader Harry Reid met in the White House on Tuesday as the clock ticked toward a midnight Friday expiration of the government’s spending authority.

“We are closer than we have ever been to an agreement. There is no reason why we should not get an agreement,” Obama said in a surprise appearance in the White House reporters briefing room.

The president said Boehner and Reid were meeting later Tuesday, but if that session produced no agreement he would summon both men back to the White House today and daily thereafter, if necessary.

“Myself, Joe Biden, my team, we are prepared to meet for as long as possible to get this resolved,” Obama said.

Obama had barely finished speaking when Boehner strode before microphones to insist that the White House and Senate Democrats bow to demands for deeper cuts.

Boehner is under extreme pressure from newly elected House members, many with allegiance to the ultraconservative tea party, to slash spending and the size of government and to lower taxes.

Short of a long-term deal, Boehner has proposed an agreement that would keep the government running for one more week and cut another $12 billion in spending. Boehner has already orchestrated action by Congress to pass a pair of stopgap bills, so far cutting $10 billion from an estimated $1.2 trillion budget to fund the day-to-day operations of government through the fiscal accounting period.

Obama said he would only accept another short-term funding extension, of two or three days, to get a longer-term deal through Congress. But he ruled out a longer extension to allow negotiations to continue.

“That is not a way to run a government. I cannot have our agencies making plans based on two-week budgets,” Obama said. “What we are not going to do is once again put off something that should have been done months ago.”

Boehner said Republicans “will not be put in a box” of accepting options they refuse to endorse.

Democrats accuse Republicans of pushing for harmful spending cuts and attaching a social policy agenda to the must-pass spending bill. Boehner counters that the White House is pressing gimmicky budget cuts.

As a government shutdown appeared increasingly inevitable, the White House has begun advising government agencies on the proper steps in preparation for a shutdown of the government.