"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, when he exhausts the bookkeeping maneuvers he has been using to keep borrowing, the threat of default would be imminent.
"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.