Bush is desperate to do something right in his last year. And he does have a great deal of power because it's American backing for anything Israel does that has allowed things to get to this state. Withdraw that unconditional support - which he can do because he's not running for office again and doesn't need to worry about upsetting the big pro-Israel lobby in the USA - and Israel might have to change its ways. So yes, it's possible.
Without Hamas being involved I don't see how there can be a lasting solution. Yes Bush can broker a deal with Israel and Fatah (Abbas) on paper but even that can come unstuck when the practicalities are involved, ie the Jewish state giving up homelands already in possession. On top of this Bush wants the Arabs to have contiguous borders and not fragmented.
Is there a solution? I believe trying to establish borders only exacerbates the problem. What about removing all borders, have just one combined state, and allow rule from one centre with all parties included. This way Israel will have peace and the Arabs will share in the wealth of the whole country.
What I cannot understand is, In his capacity as Envoy to the Middle East, why wasn't Tony Blair by Bush's side for the photo calls? Not like our grinning Tony to miss out on such an opportunity.
To answer your point Tony was in France sucking up to Sarcozy hoping to be nominated for President of the EU. The problem was Sarcozy is of the Thatcher mould and right wing so having to appease the socialists in France requires inpenetrable spikes whilst sitting on the fence.