WASHINGTON — The United States could default on its debt sometime in October if Congress does not take action to raise or suspend the debt limit, Treasury Secretary Janet L. Yellen warned on Wednesday.

The “extraordinary measures” that the Treasury Department has been employing to finance the government on a temporary basis since Aug. 1 will be exhausted next month, Ms. Yellen said in a letter to lawmakers. She added that the exact timing remained unclear but that time was running out to avert an economic catastrophe.

“Once all available measures and cash on hand are fully exhausted, the United States of America would be unable to meet its obligations for the first time in our history,” Ms. Yellen wrote.

To delay a default, Treasury has in the last month suspended investments in the Civil Service Retirement and Disability Fund, the Postal Service Retiree Health Benefits Fund and the Government Securities Investment Fund of the Federal Employees Retirement System Thrift Savings Plan.

The distribution of pandemic relief payments this year and uncertainty over incoming tax payments this month have made it more challenging than usual to predict when funds will run out. Ms. Yellen said that a default would cause “irreparable harm” to the United States economy and to global financial markets and that even coming close to defaulting could be harmful.

“We have learned from past debt limit impasses that waiting until the last minute to suspend or increase the debt limit can cause serious harm to business and consumer confidence, raise short term borrowing costs for taxpayers and negatively impact the credit rating of the United States,” she wrote.

Democratic leaders have been insisting for months that Republicans join them in raising the debt ceiling, saying the government hit its last debt limit because of the spending and tax cutting of the Trump administration, what Speaker Nancy Pelosi of California on Wednesday called “the Trump credit card.”

But Senator Mitch McConnell of Kentucky, the Republican leader, has been just as emphatic that no Republican will help Democrats on the issue.

The showdown has once again put the parties into a game of chicken, with a debt default and potential economic crisis as the consequence.

Ms. Pelosi, at her weekly news conference on Wednesday, said emphatically that Democrats would not include a statutory increase in the government’s borrowing authority in a budget bill being drafted this month. That bill, under complicated budget rules, could pass without Republican votes in the Senate.

Instead, Democratic leaders will dare Senate Republicans to filibuster a bill that does raise the debt ceiling.

“We Democrats supported lifting the debt ceiling” during the Trump administration, she said, “because it was the responsible thing to do.” She added, “I would hope that the Republicans would act in a similarly responsible way.”

Democrats have several options they are considering. The government will run out of operating funds at the end of the month, so a debt ceiling increase could be attached to a stopgap spending measure — meaning a Republican filibuster would not only jeopardize the government’s full faith and credit, it could shut down the government.

Democrats could also attach it to a major infrastructure bill that passed the Senate with bipartisan support and is supposed to get a House vote by Sept. 27.