Something which occurred to me - a bit without precedent but possibly legal...

Congress has the power, with a 2/3 vote, to expel a member. How about, instead of playing chicken with the world economy and our jobs, they put their own jobs on the line: scrap the existing debt limit and replace it with a rule of procedure in both houses that says if the House and Senate can't prevent breach of the debt ceiling (moved as they feel is necessary) they're all expelled.

Obviously it'd need to be worded such that a veto couldn't force out congress, but that sounds doable.