Mr. Geithner appeared to be playing a role not unlike that of Ben Bernanke, the chairman of the Federal Reserve, who warned lawmakers in the fall of 2008 that unless Congress voted to bail out the banking system, the credit crisis threatened to plunge the United States into a depression. Stunned by Mr. Bernanke’s dire depiction, the lawmakers undertook measures that were until then unthinkable.

In addition to his warnings about the cost of a default, officials said, Mr. Geithner told the lawmakers the White House did not believe it had the authority, under the Constitution, to continue issuing debt if it reached the debt ceiling. Nobody in the room disputed Mr. Geithner’s bleak assessment, the officials said.