Speaker Mike Johnson came under mounting pressure on Thursday from House G.O.P. hard-liners to renege on the spending deal he struck with Democrats over the weekend for avoiding a government shutdown, as ultraconservatives demanded he put forward a new plan with deeper cuts.

After meeting privately in his office in the Capitol with Republicans irate about the spending agreement, Mr. Johnson said he was discussing their demand to walk away from the bipartisan agreement but had “made no commitments” to do so.

But Republicans made it clear that they considered the deal the speaker negotiated a nonstarter, and threatened to wreak havoc in the House if he did not advance a different one. They are pressing for deep spending cuts, and many have said they cannot vote for any government funding measure that fails to include a severe crackdown on immigration.

“It’s a bad deal,” Representative Marjorie Taylor Greene, Republican of Georgia, said of the plan Mr. Johnson has agreed to with Democrats. “It’s a deal that I don’t support and other conservatives in the conference don’t support. So he’s going to have to go back to the drawing table.”