With the September 30 end of the federal fiscal year approaching, congressional staffers are becoming increasingly pessimistic about the possibility of another government shutdown unless a dozen separate appropriations bills are passed by the House.

One of the rules established during the speaker elections in January was that the House would need to pass 12 individual appropriations bills, one for every month of the year. As part of the debt ceiling deal between Speaker McCarthy and President Biden, spending will be cut by 1 percent across the board if Congress can’t pass all 12 appropriations bills by December 31.

While the debt ceiling deal set federal spending caps that were supported by most Democrats in the House and both parties in the Senate, Republicans in the House are currently aiming to cut spending by another $120 billion.

“The Fiscal Responsibility Act set a top-line spending cap — a ceiling, not a floor — for fiscal year 2024 bills,” Congresswoman Kay Granger said. “That is why I will use this opportunity to mark up appropriations bills that limit new spending to the fiscal year 2022 top-line level.”

Ms. Granger is not acting alone. She has support from the right flank of the Republican conference and has received minimal pushback from leadership so far.

Mr. McCarthy has called on members of his conference to compromise on the spending levels, even though members of the upper chamber have signaled they intend to support spending levels outlined in the debt ceiling deal.

Democrats in the House have already begun to attack Republicans for their plan to cut spending further. Congresswoman Rosa DeLauro, the top Democrat on the Appropriations Committee, told the news outlet Government Executive that Republicans pushing for further cuts were “wasting everyone’s time.”

“If we disregard the law of the land, we all but guarantee a shutdown in October,” Ms. DeLauro said. “No one who has an even basic understanding of how our process works thinks this house of cards will not get blown over the second we start a conference negotiation.”

Congressional staffers appear to share Ms. DeLauro’s views on the topic, according to a Punchbowl News survey conducted with Locus Street Group. The survey found that 79 percent of senior staffers on Capitol Hill think Congress will fail to pass all 12 appropriations bills by the end of the year.

It’s also not clear if Congress will pass even one appropriations bill to prevent a government shutdown before the fiscal year ends at the close of September.

The White House has signaled that, even if a bill at the lower spending levels some in the GOP are pushing for makes it through Congress, Mr. Biden’s signature would be far from guaranteed.

“We made a deal, and we will uphold our end of this deal,” the White House press secretary, Karine Jean-Pierre, said. “And so they need to uphold theirs.”