A handful of hard-right Republican lawmakers said on Monday they would oppose a deal to raise the United States' $31.4 trillion debt ceiling, in a sign that the bipartisan agreement could face a rocky path through Congress before the U.S. runs out of money next week.

Although expected, the opposition illustrates the hurdles that Democratic President Joe Biden and top congressional Republican Kevin McCarthy will have to overcome to see the Republican-controlled House of Representatives and Democratic-controlled Senate pass the package.

Florida Governor Ron DeSantis, a candidate for the Republican 2024 presidential nomination, said the deal does not do enough to change the fiscal trajectory. "After this deal, our country will still be careening toward bankruptcy," he said on Fox News.

Still, backers predicted it would clear Congress before the United States runs out of money to pay its bills, which the Treasury Department says will happen on June 5.

"This thing will absolutely pass. There's no question about that," said Republican Representative Dusty Johnson, who said he had talked to dozens of fellow lawmakers.

Biden said he had been working the phones, as well. "It feels good. We'll see when the vote starts," he told reporters.

The 99-page bill would suspend the debt limit through January 1, 2025, allowing lawmakers to set aside the politically risky issue until after the November 2024 presidential election. It would also cap some government spending over the next two years.

McCarthy said Monday that a historic $2.1 trillion spending cut was in the debt ceiling deal. 

A crucial first test will come on Tuesday, when the House Rules Committee takes up the bill, in a necessary first step before a vote in the full House. 

Representative Chip Roy said on Tuesday he did not support the bill. "It's not a good deal. Some $4 trillion in debt for - at best - a two-year spending freeze and no serious substantive policy reforms," Roy wrote on Twitter.

In the Senate, Republican Mike Lee also came out against the bill, which could point to a difficult vote there, where any member has the power to delay action for days. Democrats control the Senate by 51-49.

Initial reaction has been positive from financial markets, which would be thrown into chaos if the United States was unable to make payments on its securities, which form the bedrock of the global financial system.

But some investors are wary that the spending cuts secured by McCarthy could weigh on U.S. growth. Investors are also bracing for potential volatility in the U.S. bond market.

(With input from Reuters)