Steve Randy Waldman at Interfluidity proposes that banks may be able to greatly diminish the economic impact of the debt ceiling not getting raised—while earning a nice profit for themselves.
The basic idea is relatively simple, although it requires us to make two assumptions. The first is that the government really can prioritize payments, delaying some and paying others (like Treasurys). The second is that the debt ceiling really is binding: no platinum coin, premium bond, or Obamabond is going to bail us out.
In that case, people and businesses owed money by the government would become involuntary creditors. The government would still owe them the money it promised but they wouldn't not get government checks on schedule. Which is to say, the government's suppliers, contractors and other creditors would find themselves holding one of the world's safest obligations—a liability backed by the full faith and credit of the U.S. government—but short on cash.
This is a situation tailor-made for bank intermediation. Banks could advance funds to companies holding government obligations that are secured by those obligations. In exchange for this liquidity provision service, banks would receive some fee.