Why don't republicans just hold a press conference and say to everyone that enough republicans are going to take the unprecedented step of voting present, or leaving the house chamber entirely, so that Obama can pass his bill with NO republican support, while requiring all, or nearly all democrats to vote for it. Then from that day forward, President Obama OWNS the economy, and the results. The CBO can score his budget, and the debt limit will be raised that amount, but no more. Then the republicans should give their prediction that the economy will tank.
After that, every week they can go out and remind people how bad things are, and who's fault it is, making sure to include all democratic senators and house members who voted for it.