The fresh estimate came in a letter to congressional leaders in which Lew urged them to move swiftly to raise the nation's $16.7 trillion debt limit.
"If the government should ultimately become unable to pay all of its bills, the results could be catastrophic," Lew said.
The government has been scraping up against the debt ceiling since May, but it has avoid defaulting on any of its obligations by employing emergency measures to manage its cash, such as suspending investments in pension funds for federal workers.
Previously, the U.S. Treasury had said those cash management tools would be exhausted around mid-October, at which time it expected to have $50 billion in cash on hand.
Lew repeated that the Obama administration wouldn't negotiate over the debt ceiling, and he warned Republicans in Congress that any plan to prioritize certain government payments over others would be "simply default by another name."
"There is no way of knowing the damage any prioritization plan would have on our economy and financial markets," he said.
Lew warned that a repeat of the brinkmanship over the debt limit seen in 2011, which led to a downgrade in the United States' pristine credit rating, would inflict even more harm on the economy now.
"If the government should ultimately become unable to pay all of its bills, the results could be catastrophic," he said.