Efforts to rescue the sinking Middle East peace process are losing support.

Influential U.S. pundits have lost faith. Those Israelis who never did believe in it are saying: we told you so.

Some Palestinians believe it is as good as dead, strangled by Israel. They talk gloomily of a moment of truth.

Middle East veterans say they have seen such hopeless spells before, and seen them lead to outbreaks of violence.

U.S. President Barack Obama warned as much on Wednesday, saying it was dangerous of Israel to continue building settlements, hampering an urgent need to return to negotiations.

Besides Hamas Islamists in Gaza, however, there is as yet no obvious groundswell of latent violence among Palestinians.

There may be a longing for new directions: suspending the hunt for an elusive peace treaty could release energy for building a better life on the truce that exists.

Palestinian Prime Minister Salam Fayyad wants to get on with founding a state without waiting for a peace deal. Israel Prime Minister Benjamin Netanyahu has already initiated moves to help build up the Palestinian economy without waiting for a pact.

These aims may be more parallel than conflicting. Whether they can overcome core issues is another question.

NO ALTERNATIVE?

However black the mood, Western envoys usually stick to the script: there is no alternative to a negotiated peace treaty.

Israeli Foreign Minister Avigdor Lieberman is working hard to deflate what he considers such illusions.

"Whoever says that it's possible to reach in the coming years a comprehensive agreement ... simply does not understand the reality," he said last month. "He is spreading illusions and in the end brings only disappointment and ... confrontation."

French Foreign Minister Bernard Kouchner laments that Israel once had a great peace movement but now "this desire has completely vanished, as though people no longer believe in it."

New York Times columnist Thomas Friedman calls the peace process "a bad play" which no one believes in any more and which runs on repetitively, in a triumph of hope over experience.

Neither side will compromise. "If the status quo is this tolerable," he says, "let them enjoy it," but without the United States.

Times stable mate Roger Cohen has joined in, saying he is so pessimistic he now agrees with Lieberman: a non-violent status quo, a truce, may be the best that can be hoped for.

Ironically, a long-term truce is what Hamas might agree to.

THIRD WAY?

Fayyad is admired in the West for a pragmatic drive to find a third way between more conflict and a final peace pact.

Palestinian detractors say he is putting the cart before the horse. However, by raising hopes of prosperity, Fayyad may bring hope to a West Bank tired of the interminable, empty peace process, provided the weak and hobbled Palestinian Authority can deliver.

Netanyahu can help, by dismantling obstacles that Israel's occupation puts in the way of normal Palestinian development.

If all he intends to permit is a "Mickey Mouse" state, Fayyad says, then the Palestinian answer will be: forget it.

Fayyad suspects the state Netanyahu has in mind would be enclosed by Israel with large areas still under Israeli control.

Israeli strategists applaud Fayyad for challenging advocates of more resistance, but caution that his bid "to create facts on the ground" may win major international support, perhaps even diplomatic recognition, if a peace treaty looks impossible.

WHAT KIND OF STATE?

Given such worries, is Israel ready to go beyond dismantling checkpoints and end its occupation? Will it, for example, permit Fayyad to build his planned international airport?

A pullout of Israeli troops and settlers from the Gaza Strip in 2005 led to an armed standoff with hostile Hamas, with 1.5 million Palestinians suffering under a tight blockade and further war possible.

How would Israel keep a West Bank state from going the same way?

"What kind of state are we talking about?" is the question Palestinians want Israel to answer, in their latest diplomatic bid for clear terms of reference before any peace talks resume.

Lieberman says there are conflicts that have not reached a comprehensive solution, yet people have learned to live with them, renouncing violence and creating long-term conditions in which core issues can be tackled later.

He mentions Cyprus, an island divided militarily for 33 years. However, Cyprus has no large population living under military occupation.

Pragmatic he may be, but Fayyad does not suggest his people can accommodate themselves to indefinite occupation, and the only way to end that condition is through agreement with Israel.

Netanyahu has persuaded columnist Aluf Benn of the liberal Israeli daily Haaretz that he has the will to achieve peace with the Palestinians. The Israeli leader, Benn wrote without elaborating, had already informed Obama of an important political move he was about to make.

The mood of crisis seems to call for some master-stroke that might rescue the peace process from death's door, save face for Obama, avert a rift with Washington and prevent the collapse of the crumbling leadership of Palestinian President Mahmoud Abbas.

(Editing by Andrew Dobbie)