In her previous letter, issued a week ago, Ms. Yellen offered the caveat that her estimates could be off because of the unpredictability of incoming government tax revenue. She said that the actual date that Treasury will exhaust the so-called extraordinary measures that she is using to delay a default “could be a number of days or weeks later.”

On Monday, Ms. Yellen did not suggest that there might be more time and she warned that failing to lift the debt limit would be disastrous for the economy.

“If Congress fails to increase the debt limit, it would cause severe hardship to American families, harm our global leadership position, and raise questions about our ability to defend our national security interests,” Ms. Yellen said.

The nation’s cash balance has been running perilously low. On Sunday, Ms. Yellen dismissed hopes that the so-called extraordinary measures that she has been using to delay a default would be sufficient to maintain normal government operations beyond mid-June.

Republicans have refused to raise the debt limit without spending cuts, forcing Democrats to the negotiating table to avoid a default that could cause a recession and financial crisis. The two sides remain far apart on key issues, including on caps for federal spending, new work requirements for some recipients of federal antipoverty assistance and funding meant to help the Internal Revenue Service crack down on tax evasion by high earners and corporations.