We finally have a date for the debt-ceiling showdown. Doomsday is expected to arrive this year between Oct. 18 and Nov. 5.

That's according to a new analysis from the Bipartisan Policy Center. At some point in those two weeks, the Treasury Department will have exhausted all its options and will no longer have enough money to meet its financial obligations. Either Congress lifts the debt ceiling or the federal government will have to default on some of its bills.

The BPC calls this the "X Date":

What happens on the 'X date'?

Technically, the United States hit its $16.699 trillion debt limit* way back on May 19. Since then, the Treasury Department has been taking a slew of “extraordinary measures”—such as tapping exchange-rate funds — to make sure the government has money to meet all of its obligations, from paying bondholders to sending out Social Security checks.

Those extraordinary measures run out on the "X Date." If that day falls on Oct. 18, then the federal government will only have enough tax revenue to pay about 68 percent of its bills for the rest of the month — and it won’t be able to borrow or scrounge up more money to make up the difference.

Note that this is all assuming Congress strikes a deal to keep funding the government's discretionary programs past Sept. 30. If Congress fails to pass another continuing resolution and the government shuts down, that might scramble the dates a bit.

Why Obama probably can't pick and choose which bills to pay

So who gets paid if we hit the "X Date"? It's unclear. During the last debt ceiling fight, some Republicans suggested that the United States should keep funding the crucial stuff and let the rest of the government shut down. “We should pass a bill out of the House,” said Sen. Pat Toomey (R-Pa.), “saying there will be certain priorities attached to certain things, namely payment of debt services and payment of our military.”

This option is known as “prioritization.” It’s the idea that the government can selectively pay some of its bills so that the nation doesn't default on, say, its payments to bondholders — a scary scenario that could roil the world's financial markets. This may sound appealing. But there’s also good reason to think prioritization wouldn't work.

Consider how the U.S. government actually pays its bills. Each and every day, computers at the Treasury Department receive more than 2 million invoices from various agencies. The Department of Labor might say, for example, that it owes a contractor $3 million to fix up a building in Denver. The Treasury computers make sure the figures are correct and then authorize the payment. This is all done automatically, dozens of times per second.

The authors of the Bipartisan Policy Center report, Shai Akabas and Brian Collins, argue that prioritization is infeasible. "It would involve sorting and choosing from nearly 100 million monthly payments," they write. There's no good way to stop paying the Education Department while making sure soldiers get paid. It's not clear that the Treasury Department even has the technical capacity to do this, let alone the legal authority.

The Obama administration, for its part, has consistently maintained that it can not prioritize payments. In 2011, Treasury Secretary Tim Geithner told Congress that prioritization was “a radical and deeply irresponsible departure from the commitments by presidents of both parties, throughout American history, to honor all of the commitments our nation has made.”

Other (unlikely) options for the debt ceiling

That leaves three other possibilities if we hit the "X Date": First, Treasury could try to buy time by merely delaying payments — agency officials deemed this the least-bad approach back in 2011. If Treasury was facing $10 billion in obligations on Monday, but only $7 billion in revenue came in, the agency could wait until it had the full $10 billion on hand before paying Monday’s bills in full. The problem is that during the delay, Tuesday’s bills are piling up. Then Wednesday’s. This tactic would quickly become unsustainable.

Second, the White House’s Office of Management and Budget could try to stem the rush of invoices coming out of government agencies. Technically, the OMB has latitude to tell federal agencies that they can’t spend funds allotted them until later in the year — a power known as “apportionment.” The hitch is that this process can take weeks to have a meaningful impact, as former OMB official Barry Anderson told me back in January. And OMB can only slow the rate of agency spending; it can’t stop it altogether.

Third, as we've discussed before, the Obama administration could try to find some extraordinary way to get around the debt ceiling. Some Democrats have suggested that Obama can just declare the ceiling unconstitutional under the 14th Amendment. Others have suggested that he should mint a platinum coin to fund the government (yes, really). But administration officials have explicitly ruled out these moves.

Treasury Secretary Jack Lew has insisted there are only two ways the debt ceiling fight can go: Either Congress lifts the debt ceiling, or the U.S. government defaults. Obama is "not going to be negotiating over the debt limit," Lew told CNBC in August. "Congress has already authorized funding, committed us to make expenditures. We're now in a place where the only question is, will we pay the bills that the United States has incurred?"

The Bipartisan Policy Center report estimates that Congress would need to raise the debt ceiling by around $1.1 trillion to allow the government to meet all of its obligations through the end of 2014.

Correction: The current debt limit is $16.699 trillion, not $16.99 trillion. Apologies for the typo.