WASHINGTON — The White House held out hope Sunday that congressional leaders still had time "to get something big done" with President Barack Obama as the deadline for raising the nation's debt ceiling drew nearer without a solution.

"I think that what is encouraging is that the leaders in Congress seem to have all agreed that we can't push to a default," White House budget director Jack Lew said. "So I think that there are many conversations going on in order to make sure that doesn't happen."

The government will exceed the current $14.3 trillion debt ceiling on Aug. 2, after which it will be in default of its obligations. The consequences could be far-reaching, with potentially higher interest rates on mortgages and car loans, a halt in Social Security checks and unsettled world financial markets.

White House and congressional aides are continuing discussions Sunday as Congress moves on two tracks to find a solution for increasing the nation's borrowing authority while reducing long-term deficits. This comes after the failure to get a deal after five straight days of meetings between Obama and congressional leaders at the White House.

"I think there's still time to get something big done," Lew said.

Republicans have rejected any plan that contains tax increases.

Lew said on NBC's "Meet The Press" that the president "made clear he wants the largest deal possible."

"He wants to do the most we can to reduce the deficit," Lew said. "But he also said that if we can't get the most done, then in addition to extending the debt we should do as much as we can."

House Republicans are preparing to vote this week on allowing an increase in the government's borrowing limit through 2012 as long as Congress approves a balanced-budget constitutional amendment.

Sen. Jim DeMint, R-S.C., called that proof that Republicans are willing to compromise and "hardly a radical idea" but the Senate's No. 2 Democrat, Dick Durbin of Illinois, said that bill doesn't have the needed support in the Senate.

"This notion that we have to change the Constitution to do what we were elected to do is just plain wrong," Durbin said. Both senators spoke on "Meet the Press."

Lew, appearing on CNN's "State of the Union," also did not like the idea.

"What these ideas do is say let's kick the can down the road so that others will deal with it," he said. "The challenge is for Washington now to do the job the American people sent us here to do."

DeMint said the United States is on course for a financial disaster and that lawmakers have "to draw a line in the sand now because a day of reckoning is going to come."

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"And the longer we put it off the bigger the problems are going to be for our country," DeMint said.

However, if it comes down to it, White House officials who say Congress won't let the United States default are "probably right on that," DeMint said.

Senators are working 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.

"Lines of communication remain open with all parties," said Brendan Buck, a spokesman for House Speaker John Boehner.

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