House Speaker John Boehner dismissed President Obama’s position on the fiscal crisis as “not sustainable” Tuesday, only hours after Obama held a non-press conference to say he was willing to compromise but not negotiate.

"What the president said today was, if there's unconditional surrender by Republicans, he'll sit down and talk with us. That's not the way our government works," Boehner said.

The speaker said he wants conversations about spending cuts to start "now," not "next week" or "next month."

It's unclear how Republicans will navigate Obama's stance going forward, with the country in week two of the partial government shutdown. Their demand is that they get some concessions -- like spending cuts -- in exchange for passing a spending bill and raising the debt ceiling.

Boehner's appeal on Tuesday was for Democrats to simply come to the negotiating table.

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"It's time for us to just sit down and resolve our differences," Boehner said. "There's no boundaries here. There's nothing on the table, there's nothing off the table."

His remarks followed Obama’s lengthy non-press conference, in which he again accused "extreme" Republican lawmakers of holding the nation for "ransom."

The president tried to stake out his position during a lengthy exchange with reporters in the White House briefing room. Even the nature of the event was unclear. Though it was not considered a formal press conference, the president answered questions from 11 reporters and spoke for over an hour.

The takeaway was that the president, while willing to talk with Republicans about "almost anything," will not do so until they pass the spending bill and debt ceiling legislation.

"I've been willing to compromise my entire political career," Obama said. "But I'm not going to breach a basic principle that would weaken the presidency, change our democracy and do great damage to ordinary people."

Obama said Tuesday he's willing to talk with Republicans about "almost anything" -- once the impasse is over.

"I'm not going to do it until the more extreme parts of the Republican Party stop forcing John Boehner to issues threats about our economy," Obama said.

The president's remarks lasted longer than many of his formal press conferences; one August press conference lasted 52 minutes. The remarks showed Obama digging in on his position that he will not negotiate until the current pair of fiscal stand-offs is over. The president put increasing pressure on Boehner, suggesting he alone is responsible for the "cloud over U.S. economic credibility" as Republicans seek spending cuts in exchange for an increase in the debt ceiling.

The president likened the GOP's stance to demanding "a ransom for doing their jobs," and said he wants to ultimately put a stop to these semi-regular stand-offs over the budget -- without mentioning that he and Senate Democrats have not struck a deal with Republicans on a bona-fide full-year budget in years.

"The greatest nation on Earth shouldn't have to get permission from a few irresponsible members of Congress every couple of months just to keep our government open or to prevent an economic catastrophe," he said.

Obama, who took questions from several White House reporters, also said he apologizes to the American people for having "to go through this stuff every three months."

The president cited "Tea Party Republicans" in his complaints, and urged Boehner to hold a vote in the House on a spending bill, claiming such a vote would immediately end the partial government shutdown. Obama said Democrats would join with some Republicans to pass it.

"Let's stop the excuses. Let's take a vote in the House. Let's end this shutdown right now," Obama said.

Earlier in the day, Obama called Boehner merely to "reiterate" that he will not negotiate. "The president called the speaker again today to reiterate that he won't negotiate on a government funding bill or debt limit increase," Boehner spokesman Brendan Buck said Tuesday.

A statement from the White House clarified that Obama "is willing to negotiate" -- once Republicans approve the budget and debt-ceiling increase.

The phone call underscores how little progress has been made in reaching a deal ever since Congress missed a deadline to pass a spending bill, triggering a partial government shutdown.

House Republican leaders appear to have eased off their demand that ObamaCare be pared back as part of any spending package.

House Republicans are introducing a bill that would create the negotiations Boehner is calling for. The bill would set up a team of House and Senate lawmakers from both parties to immediately start talks on the debt ceiling and other fiscal issues. The bill would also ensure pay for so-called "essential" government employees who are working through the partial shutdown.

"In a divided government, the American people expect us to work together," House Republican Leader Eric Cantor said.

The White House threatened a veto of both measures.

Democrats immediately cast doubt on the idea, with one likening it to the "super committee" that failed to reach an agreement to avert steep spending cuts known as the "sequester."

Rep. Xavier Becerra, D-Calif., questioned whether a new committee on the debt ceiling would produce similar results.

Though the partial shutdown was initially triggered by disagreements over a budget bill -- and Republicans' demand that it include changes to ObamaCare -- lawmakers are shifting their focus to an Oct. 17 deadline to raise the debt ceiling.

Boehner and other GOP leaders are demanding spending cuts in exchange for raising that limit. But on this, as well as the budget, Obama and Senate Majority Leader Harry Reid say they will not negotiate.

Reid, though, said he would negotiate down the road.

"If Republicans want to propose a legislative way to make the (health care law) better or more efficient, Democrats are willing to talk about that. But shutting down the government and hoping that will make ObamaCare disappear is truly magical thinking," he said. "Democrats are willing to negotiate -- on the budget, on ObamaCare, you name it. And we're willing to compromise. But first, Republicans must reopen the government and stop threatening a catastrophic default on the nation's bills. They must respect the Democratic process."

Democrats controlling the Senate, meanwhile, plan to move quickly toward a vote to allow the government to borrow more money, challenging Republicans to a filibuster showdown as the time remaining to stop a first-ever default on U.S. obligations ticks by.

On Tuesday night the Senate Democrats unveiled a "clean" debt ceiling bill that would suspend the debt limit until Dec. 31, 2014, setting the table for a test vote later in the week.

" I hope we can get Republican cooperation to move this bill quickly," Reid said. "If not, the process could take us dangerously close to economic chaos.”

The Associated Press contributed to this report.