WASHINGTON (AP) — President Barack Obama and U.S. lawmakers pushed separate plans to avert an unprecedented default on America’s national debt, with no signs of an immediate breakthrough.

Obama called on lawmakers to approve a giant package that would not only prevent a default by raising the government’s borrowing limit, but also slash trillions of dollars from the country’s enormous deficit. He challenged lawmakers “to do something big.”

Obama used his weekly radio and Internet address to make an appeal to the public in hopes of influencing a deal that talks have failed to produce so far,

“We have to ask everyone to play their part because we are all part of the same country,” Obama said Saturday, pushing a combination of spending cuts and tax increases that has met stiff resistance from Republicans. “We are all in this together.”

Obama said the wealthiest must “pay their fair share.” He invoked budget deals negotiated by Republican President Ronald Reagan and Democratic House Speaker Tip O’Neill, and Democratic President Bill Clinton and Republican Speaker Newt Gingrich.

“You sent us to Washington to do the tough things, the right things,” he said. “Not just for some of us, but for all of us.”

As a critical Aug. 2 deadline approached, the chances that Obama would get $4 trillion or even $2 trillion in deficit reduction on terms he preferred were quickly fading as Congress moved to take control of the debate.

Opposition Republicans, who control the House of Representatives, prepared to vote this coming week on allowing an increase in the government’s borrowing limit through 2012 as long as Congress approved a balanced-budget constitutional amendment, which is highly unlikely.

In the Senate, the Republican and Democratic leaders worked on a bipartisan fallback plan that would allow Obama to raise the debt limit without a prior vote by lawmakers, discussions that now have expanded to include House officials and White House aides. The talks focused on how to address long-term deficit reduction in the proposal in hopes of satisfying House Republicans.

That plan was likely to include limits on spending across thousands of government programs, and possibly a down payment on cuts, as well.

In the Republicans’ address Saturday, Sen. Orrin Hatch of Utah argued for passage of a balanced-budget amendment. He blamed Democrats for failing to embrace adequate budget cuts and said “the solution to a spending crisis is not tax increases.”

An amendment that requires a balanced budget, he said, “would put us on a path to fiscal health and would prevent this White House or any future White House from forcing more debt on the American people.”

Even as he pushed for a more sweeping measure, Obama didn’t rule out the Senate’s more modest plan.

“We are obviously running out of time,” he told a White House news conference on Friday. It was his second news conference of the week, a testament to the overriding political and economic significance of the issue that has convulsed Washington this summer.

The government said Friday it was using its last stopgap measure to avoid exceeding the current $14.3 trillion debt limit. Administration officials, economists and the financial markets have warned that missing the Aug. 2 deadline and precipitating a government default would send convulsions through an already weakened economy.

At his news conference Friday, the president argued that he had the public on his side in calling for a large deficit reduction package that included spending cuts and increased tax revenues. But Republicans have flatly rejected any proposal from Obama that contains additional revenue from closing tax loopholes, restricting the value of deductions for the rich, increasing tax rates for hedge fund managers or ending oil and gas subsidies.

“This is not a matter of the American people knowing what the right thing to do is,” Obama said. “It’s a matter of Congress doing the right thing and reflecting the will of the American people.”

Republican House Speaker John Boehner had earlier shown some flexibility on closing tax loopholes as part of an unprecedented deal with Obama, but many Republican lawmakers are adamant that deficit reductions be limited to spending cuts.

“There are going to be no tax hikes because tax hikes destroy jobs,” Boehner said.

Both parties want to resolve the debt crisis ahead of next year’s congressional and presidential elections. Obama is seen as a candidate that is tough to beat, but voters’ fears over the economy have been dragging down his numbers.

Obama had held five straight days of meeting with congressional leaders at the White House, but none of the three options he proposed — deficit cuts of $4 trillion, $2 trillion or $1.5 trillion over 10 years — were unlocking enough support to increase the debt ceiling by the $2.4 trillion Obama wants to make it last beyond the 2012 elections.

Essentially declaring those discussions over, Senate Republican leader Mitch McConnell said Friday: “Now the debate will move from a room in the White House to the House and Senate floors.”

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Associated Press writers Alan Fram, Jim Kuhnhenn, Stephen Ohlemacher, Andrew Taylor and Erica Werner contributed to this story.

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Copyright 2011 The Associated Press.