If the two-state solution is frustrated by apparently intractable conflicts and political fragmentation, three other options are available: managed uncertainty, a Greater (and undemocratic) Israel, and a single binational state.
A first approach would be to try to continue managing the state of uncertainty that has lasted for more than 40 years. Without hope of resolution, perhaps managing the status quo–proceed with talks, occasionally reach partial agreements about nuts-and-bolts issues–is the best we can expect. Rather than focusing on resolving the conflict and detailing plans for doing so, making minor improvements and containing violence would be the more immediate goals. U.S. officials would try to build trust between Israelis and Palestinians and improve the Palestinian economy while promoting better governance.
That may sound much like the two-state approach, and there is overlap. But while efforts at economic and security improvement would continue, the emphasis and rhetoric would shift. There would be no time table for or expectation of resolving final-status issues such as the future of Jerusalem or refugees. There would be no grand plans or detailed blueprints. The time frame would be generational, with the hope that the situation would not get worse and might get marginally better.