Treasury Secretary Timothy F. Geithner said that even if he uses “extraordinary measures” to prevent the United States from defaulting on its obligations, lawmakers will need to raise the legal limit on government borrowing by July 8.

Current projections show the United States will reach its $14.3 trillion cap on borrowing “no later than May 16,” Geithner wrote in a letter Monday to leaders on Capitol Hill. He said that he would “use all measures available to me” to delay additional borrowing above that cap.

But with the national debt rising on average by $125 billion a month, those financial maneuvers would buy less than eight weeks for Congress to act.

“Default by the United States is unthinkable,” Geithner wrote. “This is not a new or partisan judgment; it is a conclusion that has been shared by every Secretary of the Treasury, regardless of political party, in the modern era.”

He said failure to raise the debt limit would result in higher interest rates and borrowing costs, falling home values and shrinking retirement savings for many Americans. He warned that default “would cause a financial crisis potentially more severe than the crisis from which we are only now starting to recover.”

The periodic debt limit increase traditionally has been a noncontroversial, almost pro forma vote to authorize the government to borrow the money necessary to pay for policies already adopted by Congress. But with the public increasingly alarmed by the rising national debt, lawmakers in both parties are eager to demonstrate their zeal for spending cuts and reluctant to authorize the Treasury to borrow more.

The Obama administration has insisted it wants an up-or-down vote on the debt limit. But it is facing increasing pressure to couple the vote with other issues, such as a long-term plan to curb government borrowing.

Numerous GOP lawmakers have indicated they won’t vote for increasing the debt limit, including, most recently, Sen. Marco Rubio (R-Fla.). But even Democrats are exerting pressure. Kent Conrad (D-N.D.), chairman of the Senate Budget Committee, has said he would not support raising the debt limit over the long term without a significant commitment to shrinking the federal deficit.

Federal Reserve Chairman Ben S. Bernanke also has offered dire warnings about the damage Congress could wreak if it fails to raise the debt limit, testifying earlier this year that default “would have extraordinarily bad consequences for our financial system. . . . It would be very destructive.”

In his letter Tuesday, Geithner also rejected suggestions that the Treasury sell off financial assets, such as a portion of the nation’s gold. “To attempt a fire sale of financial assets in an effort to buy time for Congress to act would be damaging to financial markets and the economy and would undermine confidence in the United States,” he wrote.

Geithner said that pulling certain levers within his power, such as suspending the sale of state and local government securities and suspending payments into pension funds for federal employees, could temporarily free up approximately $165 billion. But even those drastic efforts, he said, would only delay the inevitable.

“There is no alternative to enactment of an increase in the debt limit,” Geithner wrote. “I hope that the leadership in both houses will help us impress upon all members the gravity of this issue and the imperative of timely action.”

Staff writer Zachary A. Goldfarb contributed to this report.