“Why go on record raising taxes on anybody if it won’t cut spending and won’t even become law?” he asked. “I haven’t found a way of supporting that.”

Ms. Pelosi was leaning hard on House Democrats to stay united in their opposition. If she succeeds, the speaker could afford about only 18 Republican defections, fewer than he has had on any major fiscal vote since Republicans took control two years ago.

Defense Secretary Leon E. Panetta was unsparing on Tuesday in his criticism of lawmakers resisting a deal to stop the military cuts.

“It is unacceptable to me that men and women who put their lives on the line in distant lands have to worry about whether those here in Washington can effectively support them,” Mr. Panetta said in a speech at the National Press Club. “We’re down to the wire now. In these next few days, Congress needs to make the right decisions to avoid the fiscal disaster that awaits us.”

Senator Rob Portman of Ohio, an influential Republican, said the Pentagon cuts would damage not only military readiness but also the fragile economy.

House Republican leaders on Tuesday night sought to assess whether the speaker’s proposal could be brought to the House floor on Thursday. Under that plan, the House would take up take up tax legislation and consider two amendments. The first would mirror a Senate-passed bill to extend the expiring Bush-era tax cuts for incomes below $250,000. That would be expected to fail, as a show to the president that his initial offer cannot pass.

A second amendment would raise that threshold to incomes below $1 million. The House may also vote on some middle ground, like the president’s $400,000.