Ezra Klein and Dylan Matthews / The Washington Post

House Speaker John Boehner abandoned talks with the White House on Friday over a landmark debt-reduction deal, throwing into chaos efforts to raise the legal limit on government borrowing just 11 days before the U.S. Treasury is due to run out of cash.

Facing the specter of the government’s first default, a furious President Barack Obama summoned congressional leaders to the White House for an emergency morning meeting.

Five proposals are in the works to avoid default — though some aren’t likely to pass, and others won’t even get as far as a vote. Read on for a synopsis of the deals that Congress is considering to raise the debt limit, ranked (as of Friday night) from most to least likely.

The McConnell and McConnell-Reid plans: Senate Minority Leader Mitch McConnell, R-Ky., proposed giving Obama the unilateral power to increase the debt ceiling, with Congress capable of blocking him if it passed and overrode his veto on resolutions condemning the increase in the limit. The idea would be to force Democrats to vote repeatedly in favor of increasing the debt ceiling, while allowing House Republicans to vote against it without forcing the U.S. government to prioritize programs or default.

House Republicans rejected this as a giveaway to the administration, so to make it more palatable to them, McConnell and Senate Majority Leader Harry Reid, D-Nev., have been working on attaching $1.5 trillion in spending cuts and an expedited congressional process for approving them to the plan.

A small deal: Negotiations between the administration and congressional Republicans uncovered between $1 trillion and $2 trillion in spending cuts that both Democrats and the Republicans could accept. Democrats would like to see these spending cuts accompanied by new revenues, but there have been some intimations that the Obama administration could accept a deal with $1.5 trillion in spending cuts and no new revenues. The most specific look we’ve gotten at these cuts came in a slideshow presented by House Majority Leader Eric Cantor, R-Va., and leaked to the press.

A big deal: In negotiations with congressional Republicans, Obama pushed for a deal to cut the deficit by $4 trillion over 10 years through a combination of discretionary cuts, changes to entitlements such as Social Security and Medicare, and revenue increases achieved through cutting tax breaks. Specific options considered as part of this plan included an increase in the Medicare retirement age, reducing the rate of growth for Social Security benefits, and cuts to the employer health care tax deduction.

Boehner and Cantor rejected the big deal in the past, and it appeared to be making a comeback — until Boehner abandoned the latest talks with the White House on Friday.

A “clean” debt-limit increase: For the first few months of negotiations, the White House stated that it wanted a “clean” increase, not paired with any spending cuts or rule changes. When it became clear Congress would not vote for this, the administration abandoned the call and started working out a deal. On May 31, the House voted overwhelmingly against a clean debt limit increase, in an attempt by House Republicans to get Democrats on record supporting it. One can argue, however, that McConnell’s proposal is essential a clean increase.

Cut, cap, balance: Rep. Jason Chaffetz, R-Utah, introduced a bill, backed by the House Republican leadership, called “Cut, Cap and Balance,” which would increase the debt ceiling in exchange for $111 billion in immediate cuts next year, statutory caps on spending, and a balanced budget constitutional amendment to that includes a spending cap of 18 percent of the previous year’s GDP and would require supermajorities to raise taxes or increase the debt ceiling. If the amendment was ratified, spending would have to drop to its lowest levels since the 1950s — despite the fact that we now have Medicare, Medicaid, more seniors, and so forth — and taxes would be almost impossible to raise.

The White House had promised to veto the bill, saying that deficit reduction does not require changes to the Constitution and that the cuts involved are draconian. On Friday morning, the Senate defeated, in a party-line vote, this House legislation.

All you need to know about the debt ceiling

The debt ceiling is a legal cap on the amount of money the U.S. Treasury can borrow to fund existing government functions. It essentially authorizes the Treasury to borrow the money necessary to pay the bills incurred by the federal government.

Where it came from: Before 1917, Congress authorized the Treasury to issue bonds for specific purposes. But that meant approving every bond separately. To fund World War I, Congress decided to give the Treasury more latitude by instituting caps on how much it could borrow through each type of bond, rather than forcing it to get every new bond approved separately. In 1939, this was changed so that most bonds were bound by the same limit, effectively creating the general debt ceiling we have today.

How it has worked: The debt ceiling has traditionally been raised as a matter of course whenever Congress passes spending bills requiring more borrowing, though the opposition party has often voted against increases to signal its opposition to the majority’s deficit spending. Between 1940 and 2010, we have increased the debt limit more than 70 times, and from 1979 to 1995, a House rule proposed by Rep. Dick Gephardt made increases automatic by raising the ceiling whenever new spending is approved. The new Republican majority repealed this rule in 1995 to use raising the debt ceiling as leverage in getting President Clinton to agree to spending cuts.

Why it’s an issue now: Currently, the debt limit is set at $14.3 trillion. Around Aug. 2, the Treasury will exhaust that borrowing authority. Because spending currently exceeds revenues by almost 45 percent, if that happens, we will either have to default on our debt or stop funding a substantial portion of the government. Congress could simply choose to raise the debt ceiling, but like the 1995 House GOP, the 2011 House GOP is insisting that it will not increase the debt ceiling without large spending cuts from President Barack Obama.

Do we need a debt ceiling? Strictly speaking, no. The debt ceiling is unique to America. In other countries, when the legislature passes a law, the Treasury is given automatic authority to carry it out. A number of former Treasury secretaries have said it should be abolished, including Larry Summers, who said, “I think that given that Congress has to approve all spending and all tax changes, there is not much logic to the debt ceiling.”

Does the debt ceiling reduce deficits? In general, no. The nonpartisan Congressional Budget Office examined this issue and concluded that “setting a limit on the debt is an ineffective means of controlling deficits because the decisions that necessitate borrowing are made through other legislative actions. By the time an increase in the debt ceiling comes up for approval, it is too late to avoid paying the government’s pending bills without incurring serious negative consequences.”

Is the debt ceiling unconstitutional? A number of commentators have suggested that the 14th Amendment, which states that “the validity of the public debt of the United States ... shall not be questioned,” renders the debt ceiling unconstitutional. Others have disagreed, saying the Constitution gives Congress the sole power “to borrow money on the credit of the United States.”

— The Washington Post