Q: What is a default?
A: In this case, a default would be the failure by the U.S. Treasury to make payments of principal or interest on its debt in a timely manner.

Q: In a given month how much does the Treasury owe as interest on its debt?

A: Roughly about $15–20 billion (more on this in a moment).

Q: How much revenue does the Treasury take in on average in a month?

A: Roughly about $200 billion.

Q: Are you saying the Treasury could pay interest on its debt 10 times over (or more) from monthly income?

A: Yes.  Therefore the likelihood of not paying interest on its debt is zero.

Q: But, what about redeeming bonds that come due?

A: As bonds come due, the Treasury would again use monthly income to pay them off. This would lower the debt owed beneath the so-called debt ceiling.  Then, the Treasury could turn around and issue debt in that amount up to the debt ceiling.

Q: Why then do Treasury Secretary Geithner and others in government make such apocalyptic statement about the horrors of default.

A: I’m afraid Secretary Geithner and others in government are doing the moral equivalent of yelling “Fire!” in a crowded theater and they are doing so for political reasons rather than financial reasons.  They simply do not want any interruptions in the bloated spending underway in Washington and they want to scare Americans into thinking the end of the world is nigh unless the gravy train keeps chugging along.

Math is hard for politicians

Now, let’s do the math to flesh out some of these points.  I know that for many politicians and pundits math is hard, but I’ll try to make it as simple as possible. If we do not raise the debt ceiling by August 2nd, we will not default on Treasury obligations.  Nor, will we have trouble making Social Security payments.  However, there would be a big drop — roughly 44% — in government spending because that percentage represents the difference between government revenues which would be about $200 billion for the full month of August and $172 billion for August if we start counting after the first week when the deadline hits.  Spending is slated to be over $300 billion that month.

Here are the numbers from an excellent and highly detailed study by the Bipartisan Policy Center (BPC) quoted in this piece [emphasis added]:

…The BPC study found that the United States is likely to hit the debt limit sometime between August 2 and August 9. “It’s a 44 percent overnight cut in federal spending” if Congress hits the debt limit, [BPC's Jay] Powell said. The BPC study projects there will be $172 billion in federal revenues in August and $307 billion in authorized expenditures. That means there’s enough money to pay for, say, interest on the debt ($29 billion), Social Security ($49.2 billion), Medicare and Medicaid ($50 billion), active duty troop pay ($2.9 billion), veterans affairs programs ($2.9 billion).

That leaves you with about $39 billion to fund (or not fund) the following:

Defense vendors ($31.7 billion)

IRS refunds ($3.9 billion)

Food stamps and welfare ($9.3 billion)

Unemployment insurance benefits ($12.8 billion)

Department of Education ($20.2 billion)

Housing and Urban Development ($6.7 billion)

Other spending, such as Departments of Justice, Labor, Commerce, EPA, HHS ($73.6 billion)

The decision to prioritize payments would fall on the Treasury department, and Powell points out it would be chaotic picking and choosing who gets paid (in full or partially) and who doesn’t…

(Source)