The smart Austin Frakt tweeted today that “reprioritization is just a word for stiffing Social Security and Medicare beneficiaries.” My first thought was “well, yeah.” My second thought was that most people surely don’t realize that. In fact, given the intentional mystification swirling around the debt ceiling (and most other financial topics), most people probably don’t really understand much at all about the implications of the United States running into the statutory debt ceiling. So here’s an attempt (offered too late in the game, I know) to aid public understanding of this, at least a little bit.

We should start by being really clear what the problem posed by the debt ceiling is. Currently, government spending—everything from Social Security benefits to Medicare reimbursements to unemployment insurance to Federal government salaries to interest payments on holders of Treasury bills (also known as government debt)—is financed in two ways: current revenues (taxes), or, by borrowing.*

Here are some numbers for 2013. Spending by the federal government will amount to about 20.8 percent of total GDP. Taxes will account for 17.0 percent of GDP (and will hence cover 81 percent of total spending). This means we’ll borrow 3.9 percent of GDP to cover the rest of our spending.

Over the years, accumulated deficits have led to a total stock of outstanding federal debt (value of Treasuries floating around in the economy) of just under $17 trillion. There is zero evidence that this debt poses any economic problem at the moment. But, the United States is odd in that it has a (largely arbitrary) legal, statutory cap on how much outstanding debt there can be at any given time, and this cap can only be raised by Congress, which has raised it more than 100 times since 1900— and 14 times since 2001. The current cap is just under $17 trillion. So, we are essentially at the cap, and, going forward this means that no new debt can be issued.

So, let’s play out what that means if the debt ceiling truly does bind the ability to issue any new debt. Going forward, all spending must be financed by revenues with none by borrowing. But revenues are only 17.0 percent of GDP, and spending is 20.8 percent. What happens now?

Turns out that’s a hugely important and uncertain question. Theoretically, one could say that every category of federal spending gets a 20 percent haircut (this would bring total spending down to the level that can be covered by revenues alone, not new borrowing). Social Security benefits go down 20 percent, Federal salaries are cut 20 percent, and 20 percent of interest payments on outstanding Treasuries are not paid.

It is this last bit—the failure to make payments on outstanding debt, or default—that has dominated attention in this debate. And it’s true—it would be a deeply risky and stupid thing to not make these payments. The past five years should have taught us that financial markets really don’t like counterparties that are unable to make full payments, and they can be shockingly fragile. Because of the specter of financial market chaos looming if debt service payments to holders of Treasuries are not made in full, there has been some talk of “reprioritization” of federal spending. This basically means that holders of Treasury bills go to the front of the line and get paid in full before any other spending happens.

Even if this could somehow work (and most people think the Treasury lacks both the ability and the authority to reprioritize payments in this way), it doesn’t solve much. Yes, we get to breathe easy that financial markets have received their payments. But, Treasuries currently account for about 1.3 percent of GDP. So this now means that non-interest payments made by the government (19.5 percent of GDP) will have to take an even slightly bigger haircut than they did before reprioritization, because revenues available to finance them after debt-holders have been paid off has fallen to just 15.7 percent.

Does it really make sense for us to make holders of U.S. Treasuries whole but stiff every other recipient of federal spending? Again, this includes Social Security beneficiaries, Medicare providers, military personnel, etc… Holders of U.S. Treasuries are by and large much, much better-off than other recipients of Federal spending.

The most common response to this is that the financial market chaos default would unleash is the real sword of Damocles hanging over the economy, so we must take this off the table. But that’s not hugely persuasive. The mechanical effect of a 3.9 percent cutback to federal spending is absolutely enormous—about double the impact of the Recovery Act and in the wrong direction. Reprioritization does not help this at all. A sudden stop on borrowing is very, very bad for the economy, but the most immediate and predictable way it’s bad does not involve financial market uncertainty, but a sudden cutback in spending.

Additionally, it should be noted that Treasury might not even have the ability to do an across-the-board haircut in its payments systems, and the only option to avoid issuing new debt to meet current payments is to stop all payments. But, of course, they have been directed by Congress to make these payments. The economic and the legal logic of all this seems very clearly to dictate the payments not stop regardless of the debt ceiling. Whether or not an accounting workaround must be constructed to meet the letter of the law is a question for a lawyer, not me.

I’ll end with one small complaint about the talking point that has become fashionable on the correct (ie, raise the debt limit!) side of this debate: That this is about “paying bills we’ve already racked up.” This does not clarify the issue at all. It refers to not being able to make debt service payments. But that is not the real problem of running into the debt ceiling. The real problem is that it binds all federal spending. Obama administration officials, for example, freely argue that they see not making full payments to Social Security recipients and other federal spending recipients as akin to “default.” This is right, and while the “paying bills we’ve already racked up” argument might make for a good talking point, it doesn’t help people realize what’s really at stake.

*A small simplification—there are fees and some other ways federal spending can be financed. But in fact, it’s dominated by revenue and borrowing.