The most likely scenario is some kind of short-term deal to allow for more negotiating.
"We don't want any kind of default. We don't want to have to get to that spot," GOP Rep. James Lankford of Oklahoma told CNN on Monday. "If we have to get to a spot and say let's do a short-term, then we have to sit down and do a short-term."
In a possible signal to Republicans on Monday, the White House indicated it has no firm stance on the length of any debt ceiling agreement, saying it preferred a longer one but the decision was up to Congress.
While an opening may exist, CNN Chief National Correspondent John King said such an outcome would rely on conservative House Republicans trusting Obama and Democrats to negotiate in good faith on issues such as Obamacare and tax reform. Right now, King noted, "that trust simply doesn't exist in Washington."
Without an agreement, the current climate of increasingly bitter and accusatory rhetoric will only worsen as the debt ceiling deadline gets closer. Pressure will mount from the business community and an increasingly fed-up American public to come up with a way to avoid default and reopen the government.
Failure to raise the debt ceiling would leave the government unable to borrow more money to pay debts it already has accrued, CNNMoney's Jeanne Sahadi reported Monday.
Instead, Sahadi's report said, lawmakers would have four options to choose from that would have to be implemented right away -- cut government spending for the military and other discretionary programs by up to 33 percent every month; cut mandatory spending such as entitlement programs by 16 percent every month, and raise taxes by up to 12 percent every month.
The outcry over Washington's political dysfunction would escalate at home and abroad, possibly motivating moderates on both sides to meet in the middle.
In the end, it will come down to political optics as much as the actual substance of a deal. House Republicans fearing a tea party primary challenge next year need some kind of political cover to raise the debt ceiling, and Obama opposes tying the issue to partisan policy issues.