As Speaker McCarthy shepherds one of the most significant pieces of legislation of his tenure through the House, he is facing criticism from both his most liberal members and his most conservative, leading to heightened concern that the GOP’s four-seat majority is incapable of banding together.

On Wednesday, House Republicans released their debt limit proposal. It reflects increased power for the body’s conservatives. The proposed cuts to federal spending on healthcare, research and development, science initiatives, climate mitigation, welfare, and education are a conservative’s dreams come true.

The plan would also halt President Biden’s student loan cancellation and end the White House’s increased funding to the Internal Revenue Service. A wide variety of Republican members from across the country have raised concerns about nearly every aspect of the bill, from food stamps to tax policy to overall spending levels.

Congresswoman Nancy Mace told the Hill she was a “lean no” after she felt she was cut out of the process. Congressman Andy Biggs said the same. Even Congressman George Santos said he was a “hard no” because, he claims, the bill would raise taxes on New Yorkers.

One of the biggest sticking points for more moderate Republicans is the issue of food stamps. In February, as the Senate began the historically bipartisan process of writing America’s farm bill, some Republicans floated the possibility of imposing new work requirements to help cut down on the number of food stamp recipients.

In the newly released debt limit proposal, Mr. McCarthy acceded to demands, of the conservative House Freedom Caucus, that the work requirement for food stamps include persons between the ages of 50 and 56. Current law requires that those between the ages of 18 and 50 prove they are employed.

The problem for some GOP House members is that food stamps disproportionately serve their own supporters. According to a study by the Center on Budget and Policy Priorities, the Republicans’ proposed cuts to food stamps would hurt people over the age of 65, disabled veterans, and single mothers more than any other groups.

One moderate House member, Congressman Marc Molinaro, told the New York Times that he would not vote for any changes to current food stamps benefits because his mother was a beneficiary when he was a child.

“I grew up on food stamps. My mom worked and worked hard, but she’s a single mom,” Mr. Molinaro said. “That is a red line for me. We’re not going to be touching or diminishing services or support for single moms.”

Among the hardest hit by cuts to the program would be Oklahoma, South Carolina, Alaska, Alabama, and Ohio — all of which were won by President Trump twice and have Republican governors and and two Republican United States Senators.

Congressman Tony Gonzales has said he would vote against the debt limit increase if Mr. McCarthy brought a hardline immigration bill to the floor. Mr. Gonzales represents an 800-mile stretch of the southern border and has long been an advocate for a comprehensive immigration strategy, not just a wall and immigration moratorium.

One of Mr. Gonzales’s Texas colleagues, Congressman Chip Roy, is leading the charge on a more restrictive immigration package that would limit the number of immigrants that could enter the country legally. Mr. Gonzales said Mr. Roy is “playing political games” and will vote against the debt limit proposal if the “unchristian” immigration bill is brought to the floor.

Representative Greg Pence — the former vice president’s brother — told Fox News’s Maria Bartiromo on Friday that he “doesn’t know the answer” regarding whether this current debt ceiling proposal can pass. Mr. Pence criticized some of his conservative colleagues, saying that they “have to talk … as adults” with Mr. McCarthy.

Mr. McCarthy sounded the alarm bells about a possible default on the national debt earlier in the week. He said President Biden’s refusal to negotiate is a threat to the economy.

In a 40-minute speech at the New York Stock Exchange Institute on Monday, Mr. McCarthy defended his debt limit plan, saying, “In the coming weeks, the House will vote on a bill to lift the debt ceiling into the next year.” Republicans will “save taxpayers trillions of dollars, make us less dependent on China, curb our high inflation — all without touching Social Security and Medicare.” Mr. McCarthy said the president “continued to hide” as Republicans sat alone at the negotiating table.

For Mr. Biden’s part, he has said that he would sit down with the speaker only after the GOP released its budget proposal, which it has not done. The White House released its plan in March.

Considering these proposals are all dead on arrival in the Senate — as Senator Schumer said following the speaker’s Manhattan event — this is more an exercise of Mr. McCarthy showing he can manage his caucus the same way Speaker Pelosi managed hers when she only had a four-seat majority.

Mr. McCarthy’s inability to address the concerns of his caucus could lead to his ouster. Congressman Eli Crane — a Freedom Caucus member who believes the debt limit proposal does not go far enough — told CNN that he has had conversations with some of his Freedom Caucus colleagues about calling for a vote of no confidence in the speaker, which could lead to another seemingly endless voting process to either retain Mr. McCarthy or choose a new leader.

“It does come up from time to time,” Mr. Crane said of the possibility of removing Mr. McCarthy. “We look at all of the alternatives and contingency plans that could play out over the next two years.”