• House Speaker Kevin McCarthy spoke at the New York Stock Exchange.
• He opened a new phase in the debt ceiling fight by saying House Republicans would pass their own stand-alone debt ceiling hike with spending cuts and stricter work requirements.
• Such a bill, if it were passed, would be dead on arrival in the Democratic-controlled Senate and in Democratic President Joe Biden's White House.

House Speaker Kevin McCarthy said Republicans will vote in the coming weeks on a bill to raise the debt ceiling for one year, while cutting the federal budget and imposing new work requirements for Medicaid and food stamps.

Speaking at the New York Stock Exchange on Monday, McCarthy said his plan would "save taxpayers trillions of dollars, make us less dependent upon China, curb our high inflation — all without touching Social Security and Medicare."

As of Monday, however, there was no bill, just McCarthy's proposal. And even if there were a bill to vote on, it's unclear whether McCarthy would have the support within his own fractious caucus to pass it.

McCarthy's slim majority means he can afford to lose only a handful of Republicans and still pass a bill without Democratic support.

Shortly after his speech, CNBC's Sara Eisen asked McCarthy if he had the support of House Republicans for the debt ceiling proposal he had just laid out. McCarthy did not say yes.

"I think I have the support of America. I'll get the party behind it," he said.

McCarthy also sought to get out ahead of claims by Democrats and even some Republicans that the stricter work requirements for food stamps he proposes are draconian.

"Don't believe anyone who says our plans hurt Americans' social safety net," he said. "We are a very generous nation. And when people fall on tough times, we'll help them. Assistance programs are supposed to be temporary, not permanent. A hand up, not a handout."

He also pitched the stricter work requirements for food aid as a way to create new workers in a tight labor market.

"Right now there are more job openings than people who are looking for jobs. You know why? It's in part because of the Biden administration work requirements," he said. "The incentives today are out of whack. It's time to get Americans back to work."

As Congress returned to Washington on Monday from a two-week recess, McCarthy found himself in an increasingly difficult position.

President Joe Biden has not budged in three months on his refusal to negotiate over the debt limit, and has so far dismissed Republican efforts to tie a debt ceiling vote to a simultaneous deal on budget negotiations.

In his speech Monday, McCarthy sought to lay the blame for any potential market fears of a default at Biden's feet.

"The longer President Biden waits to be sensible to find an agreement, the more likely it becomes that this administration will bumble into the first default in our nation's history," he said.

Biden, meanwhile, has demanded that House Republicans produce their own budget as a starting point to negotiations. But getting his entire caucus — whose members disagree on what to cut and by how much — to sign on to one budget blueprint would be a herculean task for the Republican speaker.

"Let me be clear, defaulting on our debt is not an option. But neither is a future of higher taxes, higher interest rates, more dependency on China and an economy that doesn't work for working Americans," said McCarthy. "Addressing the debt requires us to come together, find common ground and reduce spending."

The fact that McCarthy was roping two unrelated legislative tasks – passing a debt ceiling hike and approving a federal budget – together as one deal remained a nonstarter for the White House.

In statement Monday morning, White House spokesman Andrew Bates accused the California Republican of "holding the full faith and credit of the United States hostage, threatening our economy and hardworking Americans' retirement."

Despite McCarthy's attempt to portray the White House as lagging behind or late to the table, the current state of affairs lines up with what a White House official told CNBC earlier this spring.

The Biden administration planned to pursue negotiations in earnest with Congress only after Tuesday's tax deadline.

At that point, the official said, the federal government would have a better idea of how much revenue was coming in from taxes, and how far it would go toward paying the country's bills. This would influence how urgently the White House would need to reach a deal with congressional Republicans.