Ahead of President Biden’s first negotiating session on the debt limit with congressional leaders, the two sides are impossibly far apart, with Democrats demanding a debt increase with no conditions attached and Republicans demanding major changes to federal spending before any such vote. 

On Tuesday, Mr. Biden will meet at the White House with the “Big Four” — the Democratic and Republican leaders of both the House and Senate. Speaker McCarthy has the full support of Senator McConnell, and Mr. Biden is staunchly backed by Senator Schumer and the House minority leader, Congressman Hakeem Jeffries, in his demand for a debt ceiling increase free of spending reform. 

On May 1, Secretary Yellen wrote a letter to the speaker saying that the Department of the Treasury’s “best estimate” is that the government “will be unable to continue to satisfy all of the government’s obligations by early June, and potentially as early as June 1,” raising the stakes for the meeting even higher. Shortly thereafter, the president invited congressional leaders to sit down at the negotiating table. 

Despite the invitation, Mr. Biden and congressional leaders stated they do not want to negotiate on budget items during the debt limit talks. Messrs. Schumer and Jeffries released a statement after Ms. Yellen’s May 1 notice calling for a “clean” debt limit with no changes to federal spending.

Mr. Biden, a Senate veteran, may have hoped to find sympathy in his old governing body. In 2011, during another tough debt ceiling negotiation, Mr. Biden worked with former Senate colleagues on a debt limit resolution after talks between the White House and Speaker Boehner fell apart. On Saturday, though, Senator Lee announced he had garnered enough signatures on a letter demanding spending reform to stall any debt limit increase in the Senate. 

Mr. Biden recently called Mr. McConnell to try to find a compromise between the White House and Senate Republicans in order to put pressure on Mr. McCarthy, hoping to rekindle some Senate comity as an end-run around the speaker. 

According to Politico, Mr. McConnell said he would not engage with the president. “My advice in private is the same as I’ve been saying publicly … quit wasting time here,” the minority leader said of his conversations with Mr. Biden. “And in the end, the deal will be made between McCarthy and Biden.”

The debt limit deadline has approached faster than most expected, with previous estimates saying the limit would be reached in either later summer or early fall. An analysis from the Penn Wharton Budget Model, which tracks federal spending and revenues, shows smaller-the-expected tax receipts for fiscal year 2023. 

By April of this year, the federal government had collected about $150 billion less taxes than the Congressional Budget Office had predicted. Of that total, payroll tax receipts showed a $117 billion shortfall and corporate profit receipts fell short by $36 billion. 

A few extreme options for avoiding default have been offered by the liberal left, including declaring the United States debt limit unconstitutional under the 14th Amendment. 

Section four of the Reconstruction-era amendment states that the “validity of the public debt of the United States … shall not be questioned.” A lawsuit recently filed against Ms. Yellen argues that the 14th Amendment requires the president to pay all necessary debts as appropriated by Congress. 

The lawsuit was filed on Monday in the Massachusetts federal district court by the National Association of Government Employees, which represents nearly 75,000 federal employees who are at risk of losing their jobs should the government default on its debts. The president of the union, David Holway, said in a statement that Mr. Biden has “no constitutional choice” on the issue of continuing to pay the nation’s public debts. 

“This litigation is both an effort to protect our members from illegal furloughs and to correct an unconstitutional statute that frequently creates uncertainty and anxiety for millions of Americans,” Mr. Holway said. 

Before the lawsuit was filed, Ms. Yellen threw cold water on such a proposal during an appearance on the Sunday talk shows, saying it would lead to a “constitutional crisis,” but still left the door open to such a solution. 

“There is no way to protect our financial system other than Congress doing its job and raising the debt ceiling and enabling us to pay our bills,” Ms. Yellen told an ABC News host, George Stephanopulous. When pressed on whether she thinks the 14th Amendment invocation is being considered by the White House, Ms. Yellen simply said that the United States “should not get to the point where we need to consider whether the president can go on issuing debt.”

One prominent legal scholar with Harvard Law School, Larry Tribe, argued in the opinion section of the New York Times on Sunday that the president does, in fact, have the power to suspend the debt limit and continue to pay the country’s bills. Mr. Tribe — who was once considered for a seat on the Supreme Court by President Clinton — said the establishment of the federal debt limit in 1917 violated the Constitution. 

Congress does not have the right to “invoke an arbitrary dollar limit to force the president and his administration to do its bidding,” Mr. Tribe wrote. During the debt limit negotiations of 2011, Mr. Tribe argued that proponents of this 14th Amendment workaround were wrong, and the president could not act unilaterally. He now says the “Republican roulette” being played by Mr. McCarthy demands an executive suspension of the debt limit.

Moderate Democrats on Capitol Hill have long called on the president to sit down with the speaker. Senator Manchin said the House has done its job and now the president must meet with lawmakers. “We will achieve a historic default and the economic whirlwind which follows if President Biden continues to refuse to even negotiate a reasonable and commonsense compromise,” Mr. Manchin said.

The calls are coming from beyond the party’s more conservative members. Senators Durbin and Klobuchar — both members of Democratic leadership — said the president should sit down with the speaker. Congresswoman Marcy Kaptur, a reliably liberal vote and the longest-serving woman in congressional history, said that Messrs. Biden and McCarthy “ought to have a nice dinner” and work out a framework. Congresswoman Debbie Dingell — an old friend of Mr. Biden’s — said the president “can’t keep waiting.”

After the House last week passed a Republican debt limit increase proposal — which mandated trillions of dollars in spending cuts and deficit reduction — Mr. McCarthy laid blame for the standoff squarely at the feet of Mr. Biden and Senate Democrats. 

“House Republicans did their job and passed a responsible bill,” he said in a statement after Ms. Yellen’s announcement of a June 1 deadline. “The Senate and the President need to get to work — and soon.”

The House passed the Republican debt limit proposal last week by a margin of 217–215, with four Republicans and all Democrats voting against the measure.