The lie is very simple: a failure to raise the debt ceiling will cause a default on American debt.
This is utterly and categorically a lie. Anyone who says otherwise is a liar.
As Senator Pat Toomey noted the other day,
Next year, about 7 percent of all projected federal government expenditures will go to interest on our debt. Tax revenue is projected to cover at least 70 percent of all government expenditures. So, under any circumstances, there will be plenty of money to pay our creditors.
Moreover, as the Congressional Research Service has noted, the Treasury secretary himself has the discretion to decide which bills to pay first in the event that a cash flow shortage occurs.
If we fail to raise the debt ceiling and do default, it will not because because of a failure to raise the debt ceiling. It will be because Barack Obama and Tim Geithner chose to default for political gain.
There's much more here