“It would be irrational not to do some planning,” said Mr. Rosengren, adding that Ms. Yellen’s background of dealing with financial stability matters makes her well placed to be as ready as possible for the fallout of a default. “The last thing you want is to be completely unprepared and have the worst outcome.”

As the debt ceiling standoff has intensified, Ms. Yellen has not been as involved in negotiations with lawmakers as some of her predecessors.

Mr. Biden tapped Shalanda Young, his budget director, and Steven J. Ricchetti, White House counselor, to lead the negotiations with House Republicans. Ms. Yellen has not attended the Oval Office meetings between Mr. Biden and Republicans.

“It doesn’t look from the outside like Yellen is playing an active role in the budget negotiations,” said David Wessel, a senior economic fellow at the Brookings Institution who worked with Ms. Yellen at Brookings. “That may be that it’s not her comparative advantage, it may be that the White House wants to do it themselves, and it may be that they want to protect the credibility of Treasury predicting the X-date.”

Ms. Yellen has taken a more behind the scenes role, briefing the White House on the nation’s cash reserves, calling business leaders and asking them to urge Republicans to lift the debt limit and sending increasingly regular letters to Congress warning when the federal government will be unable to pay all its bills.