In fall 2001, assigned as a State Department adviser to Middle East envoy Tony Zinni, I asked the general why he wanted to ruin a brilliant career by taking on the Israeli-Palestinian issue. Smiling, he replied that he liked hopeless causes. In that case, I said, he’d come to the right place.

Tuesday’s three-way meeting in New York among President Barack Obama, Prime Minister Benjamin Netanyahu and President Mahmoud Abbas strongly suggests that after six months of hard labor, another great American — George Mitchell — is being ground up in the maw of the Israeli-Palestinian conflict.

The problem isn’t the man: Mitchell is a talented, tough-minded negotiator. The problem is the mandate. To all but the interminably obtuse, the prospects of a conflict-ending solution between this Israeli government and this Palestinian Authority are slim to none.

And the way to get there (if there is a way) isn’t through the confidence-building measures that the administration has pursued since the spring. Even if Obama were to succeed in delivering these (a partial settlements freeze and partial normalization by the Arabs toward Israel), it would likely have little effect on the galactic task at hand: negotiating an agreement on borders, security, Jerusalem and refugees between a divided Palestinian national movement (a Palestinian Humpty Dumpty, really) and an Israel that still doesn’t know what price it’s prepared to pay to end its conflict with the Palestinians.

On paper, the approach the administration has followed in recent months seemed reasonable: Get the Israelis to freeze settlements and the Arabs to take steps toward normalizing relations.

In practice, however, neither Israel nor the Arabs were prepared to do enough to make a real difference. The administration didn’t help itself by publicly calling for a comprehensive freeze, including natural growth — an objective that was never attainable and now will lead to predictable disappointment when it can’t be reached. Nor were the Saudis, weak and vacillating, prepared to stand up without more from Israel or the United States.

Moreover, we’ve seen the confidence-building movie before; it was called Oslo. It didn’t work then, and it’s unlikely to work now. Reciprocal steps designed to create trust usually undermine it because they’re not substantial enough, are rarely offered in good spirit and are not related to the politics of the endgame, particularly nine years after Israeli-Palestinian negotiations on the core issues began during the Clinton administration.

Tuesday’s trilateral meeting may even lead to negotiations at some point. But it won’t make the administration’s next decision any easier. Negotiations on borders, Jerusalem, refugees and security will almost certainly deadlock because the gaps between Israelis and Palestinians (with a possible exception of territory) are wider than the Grand Canyon.

Obama may soon face a tough choice: whether to get out of the serious peacemaking business and manage a process as best he can or get more deeply involved and consider an unprecedented American effort to bridge the gaps in pursuit of an Israeli-Palestinian peace agreement.

I don’t envy him. The option of doing either too little, on one hand, or too much, on the other, is never good. But such is the conundrum created in part by the administration’s decision to raise expectations and by the complexities inherent in trying to solve the problem of the much-too-promised land.