"When I previously wrote to you in December, I estimated that Treasury would exhaust extraordinary measures in late February or early March," Lew wrote in a letter to House Speaker John Boehner, R-Ohio, and the other top three congressional leaders.
"Based on our best and most recent information, we believe that Treasury is more likely to exhaust those measures in late February," said the letter, which can be found at tinyurl.com/UPI-Lew-letter.
A surge of February spending, mainly for 2013 tax refunds, will leave the Treasury with little room to maneuver after the official debt limit is reached Feb. 7, he said in the letter.
As recently as last week, Senate Majority Leader Harry Reid, D-Nev., said he thought the debt-ceiling fight could be put off until as late as May.
But Lew said the government shutdown delayed the start of tax season and will concentrate refund payments, giving the Treasury little room to maneuver to keep financing the government.
"Protecting the full faith and credit of the United States is the responsibility of Congress, because only Congress can extend the nation's borrowing authority," Lew said in the letter.
"No Congress in our history has failed to meet that responsibility," he said. "I respectfully urge Congress to provide certainty and stability to the economy and financial markets by acting to raise the debt limit before Feb. 7, 2014, and certainly before late February."
Boehner spokesman Michael Steel said in a statement Republicans would need concessions from Democrats before they'd agree to raise the borrowing limit.
"The speaker has said that we should not default on our debt, or even get close to it, but a 'clean' debt limit increase simply won't pass in the House," Steel said. "We hope and expect the White House will work with us on a timely, fiscally responsible solution."
President Obama has said he will not negotiate over the debt limit, calling it a congressional responsibility, not a bargaining chip.
He maintained that position during October's 16-day government shutdown, which ended when Congress passed a temporary measure to fund the government until Jan. 15 and suspend the debt ceiling until Feb. 7.
Congress resolved the issue of funding the government when it passed an omnibus spending bill last week. But lawmakers left the debt limit untouched.
House Republicans say they intend to discuss the debt-limit matter when they gather for their annual planning retreat in Maryland next week.