Should the Congress be unable to raise the debt limit, the United States will default on its financial obligations. Such a default would have catastrophic consequences for many Americans, and the nation would be pushed over the edge into oblivion. A severe enough crisis could even lead to the declaration of martial law.
The government needs a little over $300 billion a month to operate, while its receipts are $180 billion, leaving approximately $120 billion a month in deficits that need to be covered. The U.S. treasury covers this monthly shortfall through the sale of U.S. Treasury bonds to the global financial markets. But its ability to sell these bonds depends on the credibility of the government itself—investors will only buy these bonds if they believe that America can pay back. If the federal government defaults on its payments, that credibility will be severely damaged. While some may still be willing to purchase U.S. debt instruments after a default, they will do so only at higher interest rates, and the value of the dollar would plummet.
In the worst-case scenario, global financial markets would start to dump U.S. treasuries en masse, causing a catastrophic global economic collapse as trillions in U.S. dollar-denominated assets would become worthless in a matter of hours. Not only would the U.S. be bankrupt, countries like China would go bankrupt as well, since many hold their wealth reserves in dollars. Of course, these countries could start to move preemptively, selling dollars and U.S. treasuries before the U.S. went over the edge. So the danger of a catastrophic selloff is possible even without an actual default—all that need happen is one major bank or government holding U.S. dollar-denominated assets starting to panic and selling those assets.