Representative Pramila Jayapal of Washington, the chairwoman of the Progressive Caucus, said at a news conference that White House officials told her on Tuesday night that House G.O.P. negotiators had rejected proposals that could have reduced the deficit by $3 trillion, including closing tax loopholes and imposing new taxes on the highest earners. Mr. McCarthy has repeatedly said that Republicans will not accept any tax increases.

“We will continue to call out and reject this reckless hostage-taking from extreme MAGA Republicans,” Ms. Jayapal said.

In an effort to pressure Mr. McCarthy and other Republicans not to accept any deal that falls short of the House-passed bill, Representative Chip Roy of Texas, an influential hard-liner, released a memo asserting that every measure in the legislation was “critical.”

“None should be abandoned solely for the quest of a ‘deal’,” Mr. Roy wrote.

Many Democrats, too, were arguing against any compromise. Their leaders announced on Wednesday that the final two members of their caucus had signed a discharge petition aimed at bypassing Republican leaders and forcing debt-limit legislation to the floor. With their 213 signatures, Democrats would need at least five Republicans to break ranks and sign the petition for it to trigger such a vote. Democratic leaders called on Republicans to show that they are not allied with the most extreme wing of their party and help advance the petition to avert an economic catastrophe.

“It does appear increasingly likely that House Republicans want a dangerous default, they want to crash the economy and they want to trigger a job-killing recession,” said Representative Hakeem Jeffries, Democrat of New York and the minority leader. “It’s my hope that five Republicans from New York or California or other moderate districts throughout the country can prove me wrong.”