WASHINGTON (AP) — President Barack Obama declared on Monday there would be no deal on raising the government’s debt limit if Republicans won’t compromise, and he said he would not sign a short-term extension — raising the stakes on volatile negotiations with the clock ticking toward an Aug. 2 deadline.

“I don’t see a path to a deal if they don’t budge. Period,” the president said in a challenge to his political opponents, accusing Republicans of having a “my way or the highway” posture on taxes.

Before heading to the White House for a fresh round of negotiations, House Speaker John Boehner said he agreed that “we cannot allow our nation to default on our debt.”

But Republican Boehner said that tax increases are a nonstarter: “The American people will not accept — and the House cannot pass — a bill that raises taxes on job creators.”

Obama, asked whether he would veto legislation temporarily increasing the debt ceiling, said: “I will not sign a 30-day, or 60-day, or 90-day extension.” The White House later confirmed that Obama meant he would veto such a bill.

“This is the United States of America. And, you know, we don’t manage our affairs in three-month increments,” the president said.

But even before Obama was finished speaking, Republicans were disagreeing with his insistence that a deficit-trimming deal include cutbacks in tax breaks for the wealthy and some big corporations. While the news conference was under way, Boehner’s office sent two emails to his news list saying tax hikes never should have been in the discussion.

The president warned that failure to reach agreement could create another recession and throw millions of Americans out of work, painting a picture of catastrophe if a partisan stalemate is not broken and Congress fails to act. He criticized politicians who say the debt ceiling doesn’t need to be raised.

“It’s irresponsible. They know better,” Obama said.

The president spoke at a White House news conference the morning after convening a rare Sunday meeting with lawmakers in the White House Cabinet Room, where he continued to push for a “grand bargain” in the range of $4 trillion worth of deficit cuts over the coming decade. That ran into Republicans’ refusal to raise taxes.

Obama conceded that Boehner, who pulled his support for a large-scale deal over the weekend, faced a potential revolt by his caucus, and suggested Republicans should take a political risk — as the president said he is.

“I am prepared to take on significant heat from my party to get something done,” Obama said, contending he has “bent over backward” to work with Republicans.

Despite the signs of stalemate, Obama also declared, “We will get this done by Aug. 2.”

At issue in the volatile debate is the strength of the U.S. economy and the political fortunes of Obama himself — as well as lawmakers — heading into next year’s elections. The administration warns of catastrophic economic results that would reverberate around the globe in addition to threatening the fragile recovery at home if the debt limit is not raised by Aug. 2, throwing the government into default for the first time.

Obama renewed his case Monday for a large deficit-cutting package that would put a historic dent in the country’s deficits by blending politically poisonous elements for both parties — tax hikes opposed by Republicans, and social service cuts that Democrats decry.

“”Pull off the Band-Aid. Eat our peas. Now’s the time to do it,” the president said.

“If not now, when?” the president asked, repeating a comment he made in private Sunday to lawmakers. The congressional leaders were meeting again later Monday at the White House, and Obama has said he’ll call them to meet every day into the partisan deadlock is broken.

The president said that without the tax increases all the burden would fall on those who can least afford it including seniors and poor children. “And that’s not fair,” Obama said, arguing that most people would agree with him.

Obama challenged Republicans to make the necessary compromises.

“What I’ve said to them is, ‘Let’s go,'” the president said, as the clock ticked down to Aug. 2.

Obama also took aim at the common GOP retort, “Where are the jobs?”

He said resolving the debt limit issue while tackling the nation’s longer-term deficit problems “can have a positive impact in overall growth and employment.”

“So what’s the holdup?” the president asked.

“It is possible for us to construct a package that is balanced, shares sacrifice, would involve both parties taking on sacred cows,” the president said, mentioning Medicare and Social Security.

Nonetheless, momentum could be on the side of a smaller measure of perhaps $2.5 trillion, due to Republican opposition to tax increases.

Last week, Boehner and Obama had private talks that led Democrats to believe the House speaker was willing to entertain revenue increases as part of a full overhaul of the tax code later this year in exchange for Democrats agreeing to stiff curbs on the growth of Medicare and lower increases in Social Security cost-of-living adjustments. But Boehner abandoned the idea Saturday night in a move that rattled the talks.

Sunday’s sometimes testy session was shorter than some had anticipated, and it’s clear neither side is willing to budge on taxes. Democrats say tax increases are a prerequisite for big spending cuts; Republicans rule out the idea unless taxes are lowered elsewhere.

The meeting Monday afternoon was expected to focus on agreements reached earlier in negotiations led by Vice President Joe Biden that resulted in tentative understandings on cuts to farm subsidies, student aid, federal workers’ pensions and domestic agency budgets, among others. But the Biden group was bitterly divided over taxes, as Republicans including House Majority Leader Eric Cantor of Virginia repulsed Democratic demands to shut down tax breaks for oil and gas companies and deductions enjoyed by the wealthy. And Republicans resisted Democratic attempts for a mechanism to guarantee the Pentagon would contribute to cuts.

Sunday’s meeting featured some tense exchanges, officials briefed on the talks said, as Democrats accused Republicans of being inflexible. And officials briefed on the talks said Obama sharply rebuked Republicans for saying there’s no time for a “grand bargain” blending new revenues with big spending cuts — including curbs to Social Security and Medicare.