Racing the debt clock, Congress is working on dual tracks while President Barack Obama appeals 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.”

In his weekly radio and Internet address, Obama said the wealthiest must “pay their fair share.” He invoked budget deals negotiated by GOP President Ronald Reagan and Democratic House Speaker Tip O’Neill — which included a payroll tax increase — 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. At a news conference Friday, Obama opened the door to a smaller package of deficit reductions without revenue increases.

Obama’s communications director, Dan Pfeiffer, said Saturday the president, Vice President Joe Biden and White House aides were discussing “various options” with congressional leaders and House and Senate aides from both parties.

The White House held out the possibility of arranging a meeting with the leaders today.

House Republicans 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 plan that would allow Obama to raise the debt limit without a prior vote by lawmakers. The talks focused on how to address long-term deficit reduction in the proposal in hopes of satisfying House Republicans.

A weekend deadline that the president gave congressional leaders to choose one of three deficit reduction options became a moot point after House and Senate leaders made it clear to the White House on Friday that they were moving ahead with their own plans.