With both Speaker John A. Boehner and President Barack Obama stuck in their corners on reopening the government, the dispute over the debt ceiling has taken center stage.

As it becomes increasingly clear that the two issues will be intertwined, the question turns to how long Obama can maintain a no-negotiation stance and whether Boehner can ultimately convince his restive caucus to vote for anything the president might sign that would avoid a default.

The White House opened the door to signing a short-term debt limit hike Monday — and didn’t immediately dismiss the idea of allowing legislative sidecars provided they aren’t a “concession” to the GOP.

Press Secretary Jay Carney said the White House was insisting that the debt limit be raised “without drama and without delay.”

But, he said: “How they do that, I’m not going to specify or rule in anything or rule out anything. … As long as they fulfill it without drama or delay, without brinkmanship, without threatening default is up to them. And — and the duration that they attach to it, again, is up to them.”

An acceptable sidecar to the White House is something on the order of the largely toothless “No Budget, No Pay” legislation that accompanied the debt ceiling hike earlier this year and came with a guarantee from Senate Democrats that they would pass a budget resolution for the first time since 2009. But, Carney said, Republicans would not be able to extract policy “concessions” such as rolling back Obamacare.

Boehner, at this point, continues to demand “cuts and reforms” in return for a debt limit hike, and he’s charged that the president risks default by refusing to talk.

Both sides have pointed to history to make their arguments. The White House has said no party has ever threatened default the way the GOP did in 2011. But Republicans did threaten to withhold support for the debt ceiling during the 1995-96 shutdown drama, and debt limit hikes have frequently been opportunities to pass budget process changes, including in 2010 when Obama signed pay-as-you-go budget rules long-sought by Blue Dog Democrats in return for their votes on a debt-limit increase.

The reality is that lawmakers in both parties have also long wanted to attach the debt ceiling to other bills because it is never a popular vote with the public.

Carney acknowledged the difficulty of the vote Monday, when he suggested that Congress might want to pass a longer-term hike to avoid having to vote on a debt limit increase again and again.

Republicans, meanwhile, continue to keep up their drumbeat that Obama must ultimately agree to something, lest he own a piece of the default.

“A senior White House staffer this morning said that the president would rather default on our debt than to sit down and negotiate,” Boehner said in a statement. “Now, the American people expect when their leaders have differences, and we’re in a time of crisis, we’ll sit down and at least have a conversation. Really, Mr. President, it’s time to have that conversation before our economy is put further at risk.”

But even if real talks were occurring — to either reopen the government or on the default — Democrats don’t trust Boehner to deliver.

“Speaker Boehner has a credibility problem,” said Adam Jentleson, Senate Majority Leader Harry Reid’s spokesman. “From refusing to let the House vote on a bill that was his idea in the first place, to decrying health care subsidies for members of Congress and staff that he worked for months to preserve, to stating that the House doesn’t have the votes to pass a clean CR at current spending levels, there is now a consistent pattern of Speaker Boehner saying things that fly in the face of the facts or stand at odds with his past actions.”

Boehner spokesman Michael Steel dismissed the broadside. “Passing a spending bill at the level required by law isn’t a ‘concession,’” Steel said in an email. “So it’s time for Senate Democrats to stow their faux outrage and deal with the problems at hand.”

Moreover, Steel said the Senate hasn’t been able to pass a debt limit increase either.

“The federal government is shut down because Democrats refuse to negotiate, and the debt limit is right around the corner,” Steel said. “A ‘clean’ debt limit increase can’t pass the Senate, let alone the House. It’s time for some Washington Democrat to step up, act like an adult, and start talking about how we reopen the government, provide fairness for the American people under Obamacare, and deal with the drivers of our debt and deficits.”

Senate Democrats, however, were getting ready to move ahead with a clean debt limit hike at least through late 2014. That measure could allow Congress to vote on motions of disapproval for tranches of debt that the president would then be able to veto. That procedure was first proposed by Senate Minority Leader Mitch McConnell, R-Ky., in the 2011 deal, effectively maximizing lawmakers’ cover.

House Republicans have yet to unveil their own debt limit bill, but have floated proposals to add a mechanism to force a tax overhaul, an approval of the Keystone XL oil pipeline and, of course, a delay in implementation of Obamacare.

When asked Monday whether a debt limit bill had been written yet, House Rules Chairman Pete Sessions, R-Texas, said, “Negatory.”

Sessions, who was coming out of a meeting with Boehner, said the bill would be written in the next 48 hours.

Matt Fuller and Niels Lesniewski contributed to this report.