Instead of creating a constitutional crisis by invoking the 14th Amendment, issue scrips that will be redeemable once the Republicans in the house decide to raise the debt limit.
It will prevent the shut down of the government and shame the Republicans for not paying the bills they've already created.
This idea is from this New York Times article.
http://www.nytimes.com/2013/01/10/opinion/an-escape-hatch-for-the-debt-c...