Foreign holders on US bonds might dump a bunch and stop buying them in the future. That would drive up the cost of borrowing and the cost of everything else, as well. BTW, you know who pays the bill if it costs the Treasury more to borrow? Taxpayers like us. The politicking over this issue has already caused a loss of confidence in the dollar, which could, in the long term, lead to a downgrade in the US credit rating. Bad news for borrowing.
A default could lead to a run on money market funds and we could see financial firms going the way of Lehman Brothers. Next thing you know, banks and investment firms aren't lending. There goes any hope of economic recovery. It goes without saying that stock markets around the world will take a nose dive. What did your 401K lose in the 2008 crash, 30%, 40%? It will be worse this time.
The government might have a partial shutdown; federal pension payments might be suspended (there goes my military pension); social security payments might be suspended (Republicans would like to see them eliminated altogether -- they thought it was a bad idea in the first place); states might cease to receive Medicaid funding; and so on. Bad news all the way around.
Now here's the kicker. It's unconstitutional (under the 14th Amendment) for the US not to pay its debts, debt ceiling or no debt ceiling. Thus, the president can declare default unconstitutional and arrange to pay the nation’s debts unilaterally. Maybe that's what Republicans are hoping for. Then they can use President Obama's "authoritarian spendthrift ways" against him in the 2012 election. Nah, they wouldn't be that crass, would they?
A good Q & A on the debt ceiling and the potential consequences of default can be found here.