Washington will be closely watching the financial markets on Monday to see if the uncompromising talk rattles Wall Street and worldwide economies just 10 days before the threat of default would be imminent.
Treasury Secretary Jack Lew 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 $16.7 trillion debt limit. Lew reiterated that Obama has no intention to link either bill to Republican demands for changes in the 3-year-old health care law and spending cuts.
A defiant Boehner insisted that Obama must negotiate if the president wants to end the shutdown and avert a default that 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.
"We're not going to pass a clean debt limit increase," the Ohio Republican said in a television interview. "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."
Boehner also said 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.
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.
Those who remain at home or are working without paychecks are a step closer to getting back pay once the partial government shutdown ends. The Senate could act this week on the measure that passed the House unanimously on Saturday.
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.
"Let me issue him a friendly challenge. Put it on the floor Monday or Tuesday. I would bet there are the votes to pass it," said Sen. Chuck Schumer, D-N.Y.
In a series of Sunday television appearances, Lew warned that on Oct. 17, he exhausts the bookkeeping maneuvers he has been using to keep borrowing.
"I'm telling you that on the 17th, we run out of the ability to borrow, and Congress is playing with fire," Lew said.
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.
"A default would be unprecedented and has the potential to be catastrophic," the Treasury report said. "Credit markets could freeze, the value of the dollar could plummet, U.S. interest rates could skyrocket, the negative spillovers could reverberate around the world."
Private economists generally agree that a default on the U.S. debt would be extremely harmful, especially if the impasse was not resolved quickly.
"If they don't pay on the debt, that would cost us for generations to come," said Mark Zandi, chief economist at Moody's Analytics. He said a debt default would be a "cataclysmic" event that would roil financial markets in the United States and around the world.
Zandi said that holders of U.S. Treasury bonds would demand higher interest rates which would cost the country hundreds of billions of dollars in higher interest payments in coming years on the national debt.
Sen. Ted Cruz, R-Texas, a force in pushing Republicans to link changes to the health care law in exchange for keeping the government running, spelled out his conditions for raising the borrowing authority.
"We should look for three things. No. 1, we should look for some significant structural plan to reduce government spending. No. 2, we should avoid new taxes. And No. 3, we should look for ways to mitigate the harms from 'Obamacare,'" Cruz said, describing the debt ceiling as an issue that is among the "best leverage the Congress has to rein in the executive."
Some Republicans, such as Rep. Steve King of Iowa, dismiss the warnings about a government default as an exaggeration, suggesting U.S. credit won't collapse and calling the talk "a lot of false demagoguery."
Asked how the standoff might end, Boehner, R-Ohio, said that he was uncertain: "If I knew, I'd tell you."
Boehner and Schumer were interviewed on ABC's "This Week," and Lew and Cruz on CNN's "State of the Union." Lew also appeared on CBS' "Face the Nation," ''Fox News Sunday" and NBC's "Meet the Press."
Associated Press writer Martin Crutsinger contributed to this report.