Congress passed a two-year budget deal on Wednesday to trim some spending cuts planned for next year, and the pact reduces the risk of a government shutdown.
(Read more: After budget approval, more 'kumbaya'?)
But the legislation does nothing to avoid a potential unprecedented U.S. debt default that could occur if Washington does not raise the borrowing cap soon.
(Read more: DC squabbling could still wreck the economy in 2014)
In October, Congress and the administration suspended a $16.7 trillion cap on borrowing until Feb. 7. If the debt ceiling isn't raised by then, Treasury will be able to juggle money between government accounts for a few weeks to keep just under the new limit.
But Lew said the department would exhaust these so-called extraordinary measures sometime between late February and early March. After then, it would no longer be able to borrow to cover its expenses.
"While this forecast is subject to inherent variability, we do not foresee any reasonable scenario in which the extraordinary measures would last for an extended period of time," Lew said.
(Read more: Cramer: 'Something up' with DC budget deal)