At this point in the negotiations over the debt ceiling, if I were the president, I would just hold the line at: "make some cuts, raise the debt ceiling and increase taxes on the rich". Let the GOP drive the economy off the cliff by refusing to deal. It would serve as a huge wake up call for people that blindly follow the GOP. When all the old Tea Partiers stop getting their government checks because the GOP is protecting millionaires who never had it better some minds may changes. For all those on the fence you are going to a long term shift from the GOP to Dems.
So Mr. President, hold the line... force them to make an uncomfortable deal... you already have many times, it is their turn.