1. It could cause a recession
Recessions, as you can see on the graph above, increase the deficit. During recessions, incomes fall, and so revenue from sources pegged to income — such as the payroll and income taxes — falls as well. What's more, recessions make more individuals and families eligible for social programs with income-based eligibility requirements, like food stamps, Medicaid, the Earned Income Tax Credit, and Temporary Assistance for Needy Families (TANF, or welfare).
There's historical precedent for this. In 1957, the debt ceiling forced the Air Force to stop paying its bills temporarily. As a result, it spent $8 billion less than was appropriated — which amounted to 1.7 percent of GDP. That, then-Brookings fellow Marshall Robinson argued, led to the recession of 1957-8, which in turn lead to a $12.4 billion deficit (as you can see on the above graph). So this is not just what economists believe would happen, hypothetically. It's what has actually happened historically when Congress played games with the debt ceiling.
2. It would cause interest rates to spike
Interest rates on bonds are a reflection of the risk involved in the debt. Debt issued by companies and governments on solid financial footing is considered safe, as there's little chance the issuer will default, and so the issuer can get away with only offering a modest return. Debt issued by companies in more trouble bears a greater risk of default, and so to get investors to bite, companies in that position need to offer bigger returns.
Hitting the debt ceiling is basically the United States shouting to the world, "we're in trouble." It's as if Apple CEO Tim Cook held a press conference and said, "Just FYI, there's an about 25 percent chance we're going to just not pay back people who own Apple bonds. We can totally afford to pay them, we just prefer not to. Act accordingly." If that happened, the interest rate on new Apple debt would soar to reflect the greatly increased risk of default.
Same thing with U.S. debt if we hit the debt ceiling. The longer we're over it, the greater the risk that the United States will have to stop paying out interest on debt, which constitutes default. So hitting the debt ceiling would cause a big spike in interest rates, which in turn means larger interest payments later on, increasing the deficit.
Again, this isn't hypothetical. A 2001 study by economists Srinivas Nippani, Pu Liu and Craig T. Schulman found that the 1995-6 debt ceiling fight raised interest rates temporarily, which, depending on the duration of the debt issued during that period, could affect federal budgets as far as 30 years in the future. The Bipartisan Policy Center found similar effects from the 2011 fight, estimating that it cost us $18 billion in increased interest payments going forward.
And those effects were only due to fights about the debt ceiling, not an actual breach. In 1979, the United States accidentally defaulted on $122 million in Treasury payments due to a software glitch. Terry Zivney and Richard Marcus argued in 1989 that this incident permanent increased interest rates by 0.6 percent, for a total cost of $12 billion. Suffice it to say, if the United States defaults due to the House not passing a debt limit increase, it'll default on far more than $122 million, and it'll cost the Treasury a whole lot more going forward.
3. Shutdowns cost money
Among many other terrible things, hitting the debt ceiling would cause large parts of the government to shut down. That, ironically, costs a great deal of money. You need someone to change all the government Web sites to say "closed," and to e-mail employees about when they're working. You need someone to handle federal employees transitioning off government benefits. You need security guards to make sure that unmanned offices full of sensitive data aren't broken into.
That adds up. The OMB estimates that the two government shutdowns in the 1990s cost over $2 billion in current dollars. That's not a huge effect relative to the effects of higher interest rates or of a recession, but it's not nothing.