Before that could happen, analysts say, the stock market would inevitably plummet. "Investors will hit the panic button on Oct. 18 if the debt ceiling has not been raised by then," said Ajay Rajadhyaksha, head of fixed-income research at Barclays. "The market will force Congress's hand."
There are precedents for such a denouement. After the House rejected initial legislation authorizing the bank bailout known as the Troubled Asset Relief Program during the financial crisis in late September 2008, the Dow Jones industrial average plunged more than 700 points in one trading session, prompting legislators to reverse course and approve a similar bill within days.
Market turbulence also helped set the stage for a deal in summer 2011 when Congressional Republicans and Mr. Obama squared off over the debt ceiling but ultimately compromised.
After largely staying on the sidelines as the budget battle approached in recent months, business leaders are also increasing warnings about the danger of a default. On Wednesday, Jacob J. Lew, the Treasury secretary, and other White House officials held a conference call with leaders of the Business Roundtable, which represents major American companies. Afterward, both Mr. Obama and Vice President Joseph R. Biden Jr. sat down to discuss the issue with Wall Street chieftains, including Lloyd C. Blankfein, the chief executive of Goldman Sachs.
(Read more: Markets brace for prospect of lengthy US shutdown)
Another option, at least in the short term, would be to issue i.o.u.'s to cover some of what is owed and buy more time. The California State government employed this tactic in summer 2009 during a fiscal showdown in Sacramento, issuing 450,000 i.o.u.'s valued at approximately $2.6 billion.
Mark A. Patterson, who served as the Treasury's chief of staff from 2009 until May 2013 said that he and other top administration officials studied various strategies before the 2011 standoff, including the constitutional path, selling gold and a trillion-dollar coin. "We would have been thrilled if we had an easy option to take default off the table," he said Wednesday. "We examined every idea and concluded that none of them would work."
The idea of invoking the 14th Amendment has been attacked on both constitutional and pragmatic grounds. Some legal scholars said that the amendment did not confer any legal authority on the president, pointing to the words "authorized by law." Pragmatically, specialists on Wall Street said questions about the legality of such bonds might cause potential buyers to eschew them.
"If there is no borrowing authority, any Treasury debt issued after Oct. 17 could become susceptible to legal challenges," Mr. Rajadhyaksha of Barclays said.
While the Oct. 17 Treasury deadline will increasingly become the focus in the days ahead, both for politicians in Washington and investors around the world, there may still be a bit of wiggle room after that, said Michelle Girard, chief United States economist at RBS. But not much.
The government's obligations are relatively light in mid-to-late October. That all changes on Nov. 1, when nearly $70 billion has to be paid for Social Security, Medicare, military paychecks and other obligations.
Without additional Treasury borrowing, "it's impossible to get beyond Nov. 1," Ms. Girard said. "And in our view, even Oct. 31 is too close to be able to sleep comfortably."
—By Nelson D. Schwartz and Charlie Savage of The New York Times