Keith Hennessey proposes a moderate debt-limit strategy for Republicans. Either Obama agrees to spending cuts or the debt ceiling gets passed with mostly Democratic party votes:
The President wants a debt limit increase, but his Democratic colleagues (especially in the House) expect they won’t have to vote for it. By turning this assumption on its head, this strategy would tell the President, “Hey, if you want your terrible policy, you’re going to have to deliver House Democratic votes for it. Good luck with that.” Either the President accepts and Republicans pound on the “Democratic debt limit increase” message every three months, or he agrees to cut spending. Either way, default risk is eliminated. Republicans will look responsible because they will be acting responsibly, and the markets couldn’t care less about which Members take political heat for casting these unpopular votes.
But the Members care. A lot.