Lets back up.
The US finances it's private debt through TNotes, TBonds, TBills etc... Some of those come due every month. That means that we need to sell some percentage of our old debt every month in addition to any new debt. Now, the Treasury paid off 7.5Trillion in maturing debt in 2013, and was forced to issue 8.3 trillion in new debt.
Roll Over Plan: Treasury Needed to Pay Off Record $7.5T in Maturing Debt in FY 2013, Issued $8.3T New Debt; Increased Net Debt $777B | CNS News
(from a right wing news source even)
And here's the interest
Government - Interest Expense on the Debt Outstanding
We're in a situation now, where half of the debt is being serviced every year. This currently costs us 400 Billion per year or 7% of the US budget. Failing to raise the debt limit will increase the price of
TNotes, TBills, and TBonds. This will immediately increase the cost to finance about half of the debt. Thus instead of 400 Billion per year, we're looking at 600-800 Billion per year to
finance our debt. This is money effectively taken out of the US economy which would take an additional 2% or so out of the GDP.
So now it's 2014. We have a bunch of problems. The US economy is now in a steep recession meaning
revenues are say
400Billion lower than 2013. Furthermore, the debt costs another 300Billion more to finance. That's like taking 700 Billion out of our current budget. At this point, the drag of government debt will make it impossible to ever grow or cut our way to a balanced budget.
At this point we'll have to inflate our way out of our debt, basically giving all of us a huge haircut. We will have effectively foreclosed on ourselves.