Treasury Secretary Janet L. Yellen on Sunday urged congressional Republicans to drop their demand that President Joe Biden cut spending in exchange for raising the nation's debt limit ahead of an estimated June 1 default deadline.

"These negotiations should not take place with a gun ... to the head of the American people," Yellen said on ABC's "This Week."

Yellen's comments are the latest demand from the Biden administration ahead of the president's meeting slated for Tuesday with House Speaker Kevin McCarthy, R-Calif., and other congressional leaders.

Since Republican lawmakers took control of the House in January, they have tried to seize on the looming deadline to extract spending cuts and other policy concessions from the White House.

Biden and House Republicans have spent weeks digging in their heals as budget officials have warned of the consequences of not reaching a deal soon. The government has already hit the current $31.4 trillion debt limit and has been undertaking complex financial maneuvers since January to pay its bills without borrowing even more money. Yellen warned Congress last week that the Treasury Department could run out of options to keep paying those bills as early as June 1 - sooner than had been expected.

The Biden administration has said it is refusing to negotiate over raising the nation's debt limit. According to one member of Congress, who spoke on the condition of anonymity to reflect private conversations after the midterms with then-White House Chief of Staff Ron Klain, the administration's position was: "You can't negotiate with people who take hostages."

That message was reinforced in late April by White House press secretary Karine Jean-Pierre, who told reporters: "Avoiding default is Congress's responsibility and they should act on it without preconditions," adding that Congress "should do that immediately."

But more recently, the administration has left the door open to a two-track negotiation whereby House Republicans extract reductions in federal spending and Biden sees the debt ceiling raised - while neither side acknowledges the actions as a quid pro quo.

Yellen reiterated Sunday that "early June is when we project that we will run out of cash, and there is a chance it could be as early as June 1." She added, "We have been using extraordinary measures for several months now, and our ability to do that is running out."

A default, she said, would trigger economic chaos and could lead to outcomes like "permanently higher borrowing costs for Americans for buying a home, buying a car."

Yellen did not rule out on Sunday the possibility that the administration could take unprecedented measures to avoid a default. "This Week" host George Stephanopoulos asked her whether a default could be avoided by the president invoking the 14th Amendment, which says: "the validity of the public debt of the United States, authorized by law ... shall not be questioned."

"Well, what to do if Congress fails to meet its responsibility?" Yellen said. "There is simply no good options. And the ones that you've listed are among the not-good options."