Boehner stepped back and announced what he called Plan B, legislation to let tax rates rise on incomes of $1 million or more while preventing increases for all other taxpayers.

Despite statements of confidence, he and his lieutenants decided late Thursday they were not going to be able to secure the votes needed to pass the measure in the face of opposition from conservatives unwilling to violate decades-old party orthodoxy never to raise tax rates.

Officials said as many as two dozen rank-and-file Republicans had made it clear they would oppose the bill, more than enough to send it to defeat given unanimous Democratic opposition.

At his Friday morning news conference several hours later, Boehner dismissed suggestions that he was concerned the turn of events could cost him his speakership.

‘‘No, I am not,’’ he said.

‘‘While we may have not been able to get the votes last night to avert 99.81 percent of the tax increases, I don’t think — they weren’t taking that out on me,’’ Boehner said of the Republican rank and file. ‘‘They were dealing with the perception that somebody might accuse them of raising taxes.’’

Boehner also said that last Monday he had told Obama he had submitted his bottom line proposal.

‘‘The president told me that his numbers — the $1.3 trillion in new revenues, $850 billion in spending cuts — was his bottom line, that he couldn’t go any further.’’

That contradicted remarks by White House Press Secretary Jay Carney, who said on Thursday that Obama has ‘‘never said either in private or in public that this was his final offer. He understands that to reach a deal it would require some further negotiation. There is not much further he could go.’’

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