Treasury Secretary Janet Yellen warned the country’s biggest bankers that a potential debt ceiling default will have repercussions beyond the financial system and insisted that the early June X-Date is real, Axios has learned.

Why it matters: The Biden administration is sounding the alarm in public and in private about the consequences of default, and the dangers in trying to cut a deal at the last moment.

• Yellen’s frank talk with bankers, like JP Morgan Chase CEO Jamie Dimon, are part of a broader effort by top Biden officials to enlist the business community to pressure congressional Republicans to raise the country’s $31.6 trillion debt ceiling before June 1.
• While some Republican senators have questioned that date, House Speaker Kevin McCarthy has seized it as a way to add urgency to negotiations.

The intrigue: The official readout of Yellen's meeting from the Treasury department included many of her previous warnings about the debt ceiling.

• But it didn't mention at least two of her closed-door comments: that private forecasters have largely confirmed her early June estimates for when the U.S. will run out of money and that borrowing costs are already getting higher.

Driving the news: Yellen made her remarks in a closed-door meeting at the Bank Policy Institute, an industry association that advocates for the country’s largest lenders, in Washington on Thursday, according to a person in the room.

• With talks proceeding between President Biden’s team and Rep. Garret Graves (R-La.), a key ally of House Speaker Kevin McCarthy (R-Calif), some progressive lawmakers are sounding the alarm about the potential direction of the talks.
• At the same time, a group of House conservatives want to break off negotiations, insisting that the debt ceiling bill the House passed last month should be their final offer.

Between the lines: Some Biden officials have been mildly frustrated that the business community hasn’t tried to do more to influence Republicans to pass a debt ceiling increase.

• But it’s unclear if the business groups – or even the markets — have that much influence with some of the most conservative members of Congress.

The big picture:Yellen has been warning about the consequences of default for months, with Biden weighing in on Wednesday before leaving for the G-7 summit in Japan.

• “It would be catastrophic for the American economy and the American people if we didn’t pay our bills,” Biden said.

What we are watching: A group of 11 Senate Democrats, led by Sen. Bernie Sanders (I-Vt.), sent Biden a letter on Thursday urging him to "prepare to exercise your authority under the 14th Amendment" to raise the debt ceiling.

• "We cannot reach a budget agreement that increases the suffering of millions of Americans," they wrote, arguing that it is "seemingly impossible to enact a bipartisan budget deal at this time."

But privately, Biden officials are deeply skeptical that invoking the 14th Amendment would forestall a negative market reaction or withstand judicial scrutiny.