He sought quick action to increase the limit, saying it was essential to protect the "full faith and credit" of the country, especially at a time of financial market turmoil.
The limit is $8.965 trillion. Unless Congress votes to raise it, the country would be unable to borrow more money to keep the government operating and to pay debt obligations coming due.
The United States has never defaulted on a debt payment but the decision on whether to raise the debt ceiling often means a prolonged battle in Congress.
Paulson wrote congressional leaders that according to data now available, the Treasury expects to reach the ceiling on Oct. 1 the first day of the new budget year.
That projection does not take into account moves the government often has to use, such as withdrawing investments from certain trust funds to create room for extra borrowing until Congress finally approves a debt increase.
This month, the Senate Finance Committee approved increasing the limit on the debt to $9.82 trillion. That boost of $850 billion would be the fifth since President Bush took office in 2001.
The House approved an increase in May. The full Senate has not acted yet.
"The full faith and credit of the United States, to which we all remain committed, is a national asset and a cornerstone of the global financial system," Paulson wrote. "In light of current developments in financial markets, which would be exacerbated by uncertainty in the Treasuries market, I urge the Senate to pass the legislation reported by the Finance Committee to increase the debt limit as soon as possible."
The national debt is the total accumulation of annual budget deficits, which must be financed with borrowed money.
Democrats blame Bush's tax cuts and the war in Iraq for pushing the record debt. Republicans defend the tax cuts and say the deficit is on a downward trajectory in part because of the economic stimulus from the cuts.
Senate Democrats are expected to use the upcoming debate on raising the limit to highlight the Bush administration's record on deficits.
The U.S. recorded four straight years of surpluses ending in 2001, Bush's first year. After that, deficits returned including a record imbalance in dollar terms of $413 billion set in 2004. The deficit has declined since. The administration sent Congress a budget in February that projects eliminating the deficit by 2012 while at the same time making Bush's first term tax cuts permanent.
Republicans campaigning to succeed Bush in the White House support his drive to make the tax cuts permanent. Democratic candidates have pledged to roll back the tax cuts received by upper-income families while offering tax relief to lower-income people.
Former Federal Reserve Chairman Alan Greenspan said in his memoirs published this week that Bush and Republicans had abandoned the GOP's conservative principles of favoring small government by failing to fight against rising government spending.
Bush said in an interview on Tuesday that he "would respectfully disagree" with Greenspan's comments. He said "cutting taxes made a significant difference" in the country's finances by spurring economic growth in the wake of a recession and the Sept. 11 attacks.
Vice President Dick Cheney, writing in Wednesday's Wall Street Journal, said Greenspan was "off the mark" by contending Bush had been fiscally irresponsible.
"The economic growth encouraged by the president's tax cuts is now producing sharply increased federal tax receipts," Cheney wrote.