"There are not the votes in the House to pass a clean C.R.," he said on the ABC program, referring to a continuing resolution to provide money for military and domestic programs.
The speaker's assessment that he did not have the votes to pass a clean budget bill was contradicted by members of both parties. "I'm positive that a clean C.R. would pass," said Representative Peter T. King, Republican of New York.
"If it went on the floor tomorrow, I could see anywhere from 50 to 75 Republicans voting for it," he added. "And if it were a secret ballot, 150."
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Senator Charles E. Schumer of New York, a Democratic leader, was just as blunt in a telephone interview. "Nobody believes that," he said of the speaker's comment.
Mr. Schumer challenged Mr. Boehner to put a clean budget bill on the floor and prove that he is right. He called the speaker's remarks "a step back."
"I'm hearing from my Republican colleagues that this is a strategy going nowhere that's hurting them and hurting the country," he added, noting that several Republicans have approached him recently asking him to help broker a deal that ends the shutdown. "What they're saying to me is we've got to help Boehner find a way out of this," Mr. Schumer said.
Mr. Boehner also said the House would not pass an essential increase in the debt limit without concessions from Mr. Obama. Republicans have said in recent days that Mr. Boehner had privately assured them that he would not allow a breach of the debt limit, though it was unclear how far he would be willing to go to avoid it.
In his television appearance, he said firmly, "We're not going to pass a clean debt-limit increase."
"I told the president, 'There's no way we're going to pass one,' " he added. "The votes are not in the House to pass a clean debt limit. And the president is risking default by not having a conversation with us."
(Read more: Moody's CEO: US default 'extremely unlikely')
Describing the negotiations he wanted with Mr. Obama, Mr. Boehner seemed to shift from demands that the president agree only to defund or delay his signature health care law — a nonnegotiable condition, as Mr. Obama sees it — to calling once again for deficit reduction talks that would result in savings from Medicare in particular.
Mr. Obama has proposed hundreds of billions of dollars in long-term savings in the entitlement programs, including Social Security, but only if Republicans agree to raise additional revenues by closing tax loopholes for wealthy individuals and some corporations.
Mr. Boehner ruled that out. "We're not raising taxes," he said.
On the budget impasse, the speaker acknowledged that in July he had gone to the Senate majority leader, Senator Harry Reid, a Nevada Democrat, and offered to have the House pass a clean financing resolution. His proposal would have set spending levels $70 billion lower than Democrats wanted, but would have had no contentious add-ons like changing the health care law.
Democrats accepted, but they say that Mr. Boehner then reneged under pressure from Tea Party conservatives.