The emerging measure is designed to ensure that there's no repetition of the current borrowing squeeze until after the 2014 elections.
Depending on the Republican response, it could be the middle of next week before a final vote is taken on the measure, close to the Oct. 17 deadline that Treasury Secretary Jacob Lew has set for Congress to avert a possible default.
The details were described by officials who spoke on condition of anonymity, saying they were not authorized to discuss a measure that has yet to be made public.
It is unclear when Republicans in the House, who hold a majority, intend to advance debt limit legislation of their own.
Republicans have said they will seek long-term deficit cuts or reforms to benefit programs and perhaps a wholesale rollback in environmental rules as the price for raising the current $16.7 trillion debt limit. President Barack Obama has ruled out negotiations on the measure, although he has said he is willing to discuss fiscal and other issues with the GOP once the weeklong partial government shutdown is over and the Treasury is free to borrow again.
Gene Sperling, a senior Obama economic adviser, was pressed on whether he would rule out a two- or three-week extension on increasing the nation's $16.7 trillion debt limit. Treasury Secretary Jack Lew has warned that on Oct. 17, he exhausts the bookkeeping maneuvers he has been using to keep borrowing.
"There's no question that the longer the debt limit is extended, the greater economic certainty there will be in our economy which would be better for jobs, growth and investment," Sperling told a breakfast sponsored by the newspaper Politico. "That said, it is the responsibility of Congress to decide how long and how often they want to vote on doing that."
Economists say a default could trigger a financial crisis and recession that would echo 2008 -- or worse. The 2008 financial crisis plunged the country into the worst recession since the Great Depression of the 1930s.
Sperling reiterated Obama's vow not to negotiate on the debt because it would sanction the threat of default as a bargaining chip and increase the chance of default in the future.
Seeking to maintain pressure on Republicans, Obama made a previously unannounced visit to the Federal Emergency Management Agency headquarters Monday to draw attention to a government agency that has had to furlough 86 percent of its workforce as part of the partial shutdown.
Obama thanked FEMA employees for their work preparing for Tropical Storm Karen, which dissipated Sunday after posing a threat to the Gulf Coast.
"We dodged a bullet there," Obama said.
FEMA recalled 200 furloughed workers last week to help prepare for the storm. Obama said that now that the storm has weakened, at least 100 of those workers will have to return to furloughed status.
"That's no way of doing business," the president said.
The Republican-controlled House last week passed legislation that would continue to direct money to FEMA during the shutdown. But Democrats and the White House say they do not want to respond to the impasse in a piecemeal fashion.
A defiant House Speaker John Boehner has insisted that Obama must negotiate on changes to the 3-year-old health care law and spending cuts if he wants to end the shutdown and avert a default.
"We're not going to pass a clean debt limit increase," the Ohio Republican said in a television interview Sunday. "I told the president, there's no way we're going to pass one. The votes are not in the House to pass a clean debt limit, and the president is risking default by not having a conversation with us."
The uncompromising talk rattled financial markets early Monday as stocks slumped. China, which holds $1.277 trillion in U.S. Treasury bonds and stands as the United States' biggest foreign creditor, urged that all efforts are made to avoid a default.
Among congressional leaders, however, animosity marked the stalemate and resolution seemed elusive.
Boehner said Sunday that he lacks the votes "to pass a clean CR," or continuing resolution, a reference to the temporary spending bill without conditions that would keep the government operating.
Democrats insist that Republicans could easily open the government if Boehner simply allows a vote on the emergency spending bill. Democrats argue that their 200 members in the House plus close to two dozen pragmatic Republicans would back a so-called clean bill, but the Speaker remains hamstrung by his tea party-strong GOP caucus.
"I ask the Speaker, why are you afraid?" Senate Majority Leader Reid said on the Senate floor. "Are you afraid this measure will pass, the government will reopen and Americans will realize you took the country hostage for no apparent reason?"
Across the Capitol, Boehner said House Republicans have repeatedly asked for negotiations over ending the shutdown and curbing the health care law, only to be turned down by Obama and congressional Democrats.
"The president's refusal to negotiate is hurting our economy and putting our country at risk," Boehner said as Monday's House debate began.
He said Americans expect that in "a time of crisis," their leaders will talk.
"Really, Mr. President. It's time to have that conversation before our economy is put further at risk," Boehner said.
Lew has warned that the budget brinkmanship was "playing with fire" and implored Congress to pass legislation to re-open the government and increase the nation's debt limit.
The shutdown has pushed hundreds of thousands of workers off the job, closed national parks and museums and stopped an array of government services.
The one bright spot on Monday is a significant chunk of the furloughed federal workforce is headed back to work. Defense Secretary Chuck Hagel ordered nearly 350,000 back on the job, basing his decision on a Pentagon interpretation of a law called the Pay Our Military Act.
In a series of Sunday television appearances, Lew said that while Treasury expects to have $30 billion of cash on hand on Oct. 17, that money will be quickly exhausted in paying incoming bills given that the government's payments can run up to $60 billion on a single day.
Treasury issued a report on Thursday detailing in stark terms what could happen if the government actually defaulted on its obligations to service the national debt, with credit markets frozen, the dollar in free fall and U.S. interest rates skyrocketing.
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