Now that the government shutdown has happened, public pressure probably will force an end fairly soon, once House Republicans find a face-saving way out that doesn’t involve the delay of the health-care law, at least for now. Then the battle over “Obamacare” (and possibly other issues) will move to the debt ceiling, where the drama will intensify.

Treasury Secretary Jacob J. Lew has urged Congress to pass a clean bill raising the debt ceiling by mid-October to avoid potentially devastating consequences for the U.S. (and possibly the global) economy. Here’s my attempt to handicap some possible outcomes on this debate, where the stakes are even higher than in the government shutdown fight.

Immediate ‘Clean’ Extension

This has long been the administration’s only position, and President Barack Obama probably would be happy with an increase in the limit that wouldn’t require another vote until after the November 2014 mid-term elections. Republicans are dug in against a clean extension, and there is virtually no chance it happens unless the nation suffers severe financial distress.

Now that a government shutdown has occurred, the debt ceiling debate is shaping up to be an even larger fight in Washington. But what are the options Congress will have to face?

During the August 2011 debt ceiling showdown, the stock market dropped steeply until a deal was reached, although the market was also affected by the Eurocrisis and a pullback in home-buying at the same time. Since a deal was eventually hammered out, the equity markets this time may — at least for a short period — believe the parties are crying wolf, unless it becomes clear that the continuing resolution (CR) debate presages an impasse over the debt ceiling, which could trigger an earlier market sell-off.

Extension With Some Conditions

The president is just as dug in against any kind of conditions for raising the debt ceiling, and his spokespeople have been adamant that they won’t accept a delay of the individual mandate under the health law. That said, his administration has indirectly opened the door to a potential delay, but not defunding, of the individual mandate by delaying the employer mandate for a year. In addition, there have been media reports about software glitches in the health insurance exchanges, which went live on Oct. 1.

Accordingly, there is some chance that the administration could agree to an individual mandate delay of some duration (to save face, the president could try to keep the delay to less than a year), or perhaps a less controversial condition (such as a timetable for a tax overhaul).

Administration Invokes 14th Amendment

So much bluster is coming from both sides of the debate that it’s difficult for outsiders to tell how seriously the parties privately take their ultimatums. Take the so-called 14th Amendment option, which a number of legal scholars — and even former President Bill Clinton — have urged Obama to invoke.

Under this approach, if Congress doesn’t raise the debt ceiling, the president would cite the opening language in the 14th Amendment that “the validity of the public debt of the United States … shall not be questioned” and order the Treasury to continue issuing debt to pay some or all of the government’s bills. However, the president also would be ignoring Article I, section 8 of the Constitution, which gives Congress the power to borrow money, and essentially daring House Republicans to sue to stop him from breaking the debt ceiling.

Administration Prioritizes Payments

Earlier this year the House passed a bill, H.R. 807, that would authorize the president, in the event of an impasse over raising the debt ceiling, to continue paying interest on the government’s bonds and Social Security benefits. Democrats voted against the bill and the president threatened to veto it (the Senate has not taken it up). The version of the stopgap spending bill, H.J. Res. 59, passed by the House on Sept. 20 also contained prioritization language.

John Boehner will have his hands full in the coming weeks as he will be tasked to negotiate an end to the government shutdown and how Congress can act on the debt ceiling

The administration has insisted it isn’t practical to try to choose which bills to pay on time, and which to let slide. However, faced with a halt in Social Security and Medicare payments, salary payments to the military and so on, the president may change his mind and order his Treasury secretary to prioritize payments in some manner.

Lawsuits brought against president to stop either the 14th Amendment or prioritization options could lead to several outcomes, most of them in Obama’s favor, notwithstanding the Article I language. The federal courts could decide that the plaintiffs lack standing (citing its increasingly narrow interpretation of standing doctrines), or that the case is a “political question” to be decided between the executive and legislative branches. My guess is that both Chief Justice John Roberts and swing vote Justice Anthony Kennedy in particular would be loath to support a decision that put the U.S. Government into default.

For the president to embrace the 14th amendment or prioritization options, he’d have to say that things are different somehow than when he previously rejected them. But don’t rule out either option; default is worse.

Any legal drama lasting more than a few days, however, would not only spook the financial markets, but also invite a “pox on both your houses” reaction from key independent swing voters, who would remember this mess when voting in the mid-term elections.

Temporary Default Followed by Compromise

The president could let default proceed, hoping that negative reaction from the financial markets and the electorate forces Republicans back to the bargaining table in a mood to compromise. At some point, of course, there will be a compromise of some sort, but in this age of divided government and bitter partisanship, we are learning that it often takes a crisis to induce political action. Leaders of both political parties may decide that this is the only way to reach a deal. If things go this far, it would be unfortunate, because it would put a stain on the debt of the U.S., and require the federal government to pay some interest premium until investors forget the sordid episode (which they might not).

Kick the Can

Finally, there is the time-honored practice of kicking the can down the road for a few more months while the parties continue to wrangle. This option could take the form of a modest lifting of the debt ceiling to get the government past the end of this calendar year. This way the parties could celebrate the new year in much the same way they did last year during the “perils of Pauline” debate that culminated in the fiscal cliff tax deal.

Bottom Line

I wish I were clairvoyant enough to know which of these scenarios is most likely. My best guess is that the parties will end up, hopefully without a temporary default-related financial crisis, kicking the can for some limited period of time. Failing that, if the public is displaying a strong “pox on both your houses” attitude, the president may end up swallowing some delay in the individual mandate under Obamacare as the price of getting a more substantial debt ceiling increase that would take the country through the midterm elections or possibly through the end of 2014.

(Robert Litan is the director of research for Bloomberg Government. You can follow him on Twitter at @BobLitan. A version of this executive outlook originally appeared Sept. 27 for BGOV subscribers.)

–Editors: Daniel Parks, Jodie Morris

To contact the analyst: Robert Litan in Washington at +1-202-416-3441 or rlitan2@bloomberg.net

To contact the editor responsible: Daniel Parks at +1-202-416-3435 or dparks9@bloomberg.net