President Barack Obama vowed not to relent to what he called Republican “extortion” that would threaten a default on the national debt, but suggested he might accept a short-term agreement that could jump-start talks with Congress.

But the nation's top elected Republican, House Speaker John Boehner, R-Ohio, described Obama's possible arrangement as akin to "unconditional surrender" to the president by Republicans.

“We can't make extortion routine as a part of our democracy,” Obama said at the White House during a press conference in which he pummeled congressional Republicans for failing to resolve the current federal government shutdown and vote to raise the debt limit before the Oct. 17 deadline.

The speaker responded a short time later, saying that it was Obama -- not him -- who was guilty of being too unyielding.

"The president's position that ... we're not going to sit down and talk to you until you surrender is just not sustainable," Boehner said on Capitol Hill. "It's not our system of government."

President Barack Obama points comments toward House Republicans over the government shutdown while speaking Tuesday at the White House.

“We're not going to pay a ransom for America to pay its bills,” the president said, arguing that default would cause a massive shock to the American economy, making loans more costly and threatening to shortchange millions of workers.

But Obama also said for the first time that even a short-term extension of both the debt ceiling and government spending would be enough for him to enter into negotiations with Republicans over a longer-term deal.

“Re-open the government, extend the debt ceiling,” Obama said Tuesday afternoon. “If they can't do it for a long time, do it for a period of time in which in which these negotiations are taking place.”

Boehner seemed to reject such a scenario, describing it as "unconditional surrender" by the GOP to the president. He sidestepped completely a question about how he would handle the debt ceiling if lawmakers went down to the waning minutes before the deadline without an agreement.

As the brinksmanship played out, the president also nodded to growing public frustration toward their elected leaders, saying that he was also tired of continued instances of brinksmanship versus Republicans in Congress. Last week, Obama called himself “exasperated” during an interview with CNBC.

“To the American people, I apologize that you have to go through this stuff every three months, it seems like,” he said. “Lord knows I’m tired of it.”

But with no resolution to the nation’s current fiscal impasse in sight, the president renewed his pledge not to negotiate with congressional Republicans over funding the federal government and paying the national debt. The president has said that an extension of both, without conditions, must be passed by Congress before he agrees to any talks with Republicans.

Indeed, the very question of whether Obama and Republicans should be negotiating in the first place has stalled any talks toward resolving this standoff. Just nine days separate the American government before the deadline established by the Treasury Department as the point by which Congress must authorize increased borrowing to meet the government’s existing obligations.

"You know, Americans expect us to work out our differences. But refusing to negotiate is an untenable position,"Boehner said earlier Tuesday on Capitol Hill. "And frankly, by refusing to negotiate, Harry Reid and the president are putting our country on a pretty dangerous path."

But in the absence of any meaningful developments to resolve a crisis that was, at once, both economic and political, the president and his Republican allies were still consumed by the business of placing political blame with each other.

Obama’s appearance in the White House briefing room was meant to marshal the power of the bully pulpit to increase pressure on Republicans to relent from their position and vote for a short-term extension of government spending without conditions. Such legislation is favored by the Democratic Senate, and the White House has been tallying the growing number of Republicans who have suggested they might consider supporting this “clean continuing resolution.”

According to a count by NBC News, as many as 21 House Republicans could support such a measure, though their support is never guaranteed until a vote comes to pass, and a number of variables could sway Republican lawmakers before then.

“My suggestion to the speaker has been – and will continue to be – let's stop the excuses, let's take a vote in the House, let's end this shutdown right now, let's put people back to work,” Obama said. As the bickering continued, Obama and Boehner chatted briefly on Tuesday morning, though the call – according to both leaders’ offices – gave way to little new consensus.

As Republicans mull their path forward, GOP leaders laid out a new plan to their rank-and-file on Tuesday, passing two bills that will be merged and sent to the Senate in an effort to begin negotiations on the debt limit.

One bill, passed unanimously, would guarantee pay for essential workers who have stayed on the job throughout the shutdown.

The other bill, passed by Republicans in a 224-197 party line vote, would establish a bipartisan negotiating team to tackle the debt limit and other fiscal issues, somewhat resembling some of the other official panels and working groups that have unsuccessfully tried to resolve the deep fiscal differences between Democrats and Republicans in recent years.

It's not clear that this group would have any greater success, though, especially since its authority is nonbinding -- unlike some of the past panels, like the 2011-2012 "supercommittee."

Of the new GOP proposal, Obama said: “The leaders up in congress, they can work through whatever processes they want, but the bottom line is either you're having good-faith negotiations in which there's give and take, or you're not.”

To boot, the White House said later in the afternoon that Obama would veto the legislation if it ever reached his desk.

Boehner dismissed talk of such a temporary resolution as "a lot of speculation," refusing to engage with a reporter's question. And the Republican speaker said that he didn't have any particular standard by which he's measuring the GOP's willingness to enter into an eventual deal.

"I'm not drawing any lines in the sand," he said, later adding: "There's no reason to make it more difficult to bring people to the table. There's no boundaries here. There's nothing on the table, there's nothing off the table. I'm trying to do everything I can to bring people together and have a conversation."

As the shutdown continued to play out, there were increasing signs that the GOP was shouldering more of the political blame for the shutdown. An ABC News/Washington Post poll released Monday found, for instance, that seven in 10 Americans disapprove of the way congressional Republicans have handled negotiations over the federal budget.

NBC News' Frank Thorp contributed reporting.

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