Two of the Senate’s staunchest fiscal conservatives said on Sunday that they would try to force significant changes to the bill passed by the House last week to deliver President Trump’s domestic agenda, signaling a precarious path ahead for the legislation.

Senator Ron Johnson of Wisconsin said on CNN that he saw the opportunity Republicans now have — with control of the House, Senate and White House — as “our only chance” to reset to “a reasonable prepandemic level of spending.”

Mr. Johnson accused the House of rushing through the process of putting the bill together and of approving legislation that would ultimately add to the deficit. And he suggested that enough of his colleagues in the Senate felt the same way to be able to enact major changes.

“I think we have enough to stop the process until the president gets serious about spending reduction and reducing the deficit,” Mr. Johnson said.

Senator Rand Paul of Kentucky, another fiscal conservative, criticized the House package, saying on “Fox News Sunday” that it lacked concrete measures to reduce the ballooning national debt. He said that the package was “not a serious proposal,” and that Republicans should cut deeper into major drivers of the debt, including Medicaid, Social Security and food assistance programs.

“Somebody has to stand up and yell: ‘The emperor has no clothes,'” Mr. Paul said. “Conservatives do need to stand up and have their voice heard.”