Three attempts were made for a two-state solution. First was the attempt during the administrations of Barak and Clinton. Clinton told Arafat that he made him a failure. Arafat walked away and started an uprising/intifada. Then A. Sharon tried unilateral withdrawal, which would lead to a two-state solution. Gaza was completely freed. He hoped this would be a first step and then he would do the same with his chosen areas of the West Bank. He had a stroke and never was able to finish his plan. Hamas kicked out The Palestinian Authority, killed several of them, and then turned Gaza into a military base to destroy Israel. Effort #2 failed. Olmert and Abbas worked on effort #3. He offered 97% of the West Bank and land swaps for the other 3%. He offered East Jerusalem as the capital for them. Abbas walked away and made Bush a failure as well. This led to the death of the left as a serious power in Israel. Her parties have less than 10% of the vote now.
The reason why the great majority of Israelis reject a two-state solution is that they know for sure that such a state would become a radical Hamas military base like Gaza. Therefore their solution is autonomy. Israel keeps overall security, the Palestinians in the West Bank have passports from Jordan or Israel but no citizenship, no army, and no statehood. It would be like Puerto Rico. They would choose local governments and the Palestinian government but not have a state. The West Bank would have Jewish areas and Palestinian autonomous zones. This is the best we can hope for but it is a long shot for there to be any solution. Also, Palestinian education would have to be deradicalized.