By Dan Williams

JERUSALEM, May 1 (Reuters) - Ehud Olmert is their most unpopular prime minister but Israelis struggle to imagine someone else would be better.

A commission of inquiry report into last year's Lebanon war that censured the government has underscored unhappiness with a generation of elected leaders and contenders deemed ill-equipped to deal with looming regional challenges.

Capturing the national mood after the Winograd Commission findings were issued on Monday, Israeli television broadcast the results of a survey in which respondents were asked: "Which politician do you consider least untrustworthy?"

Olmert ranked predictably low. He had been described by the panel as responsible for the failings of the assault on Lebanese Hezbollah fighters and is dogged by corruption scandals.

Yet even his most highly-regarded rival in the poll, leftist ex-admiral Ami Ayalon, polled only 45 percent.

"The bottom line is that Ehud Olmert has to go," said Nahum Barnea, a pundit with Israel's Yedioth Ahronoth daily.

"With that said, he can still survive politically -- not because the war was a success but because the alternatives, even by the commission's standards, aren't any better."

Despite single-figure approval ratings, Olmert has vowed to stay on. He commands a broad governing coalition that will likely buttress him against any rebellion in parliament.

Yet some analysts point to wider Israeli realities, be they a problematic electoral system or growing public apathy, as preventing a significant challenge to Olmert's hold on power.

There is also fatigue with the high turnover of national leaders. This cycle has, over the decades, run parallel to Israel's fortunes in war and often favoured former generals over career politicians like Olmert and Defence Minister Amir Peretz.

"I am saddened, today, to see how much the people of Israel enjoy the need to 'execute' their leaders," said Haifa Mayor Yona Yahav, whose northern city suffered Hezbollah rocket salvoes during the 34-day conflict.

NETANYAHU AWAITS

One member of Olmert's cabinet quit on Tuesday and called on the prime minister to do the same, but a better gauge of public spirit might be in the turn-out at an anti-government rally planned for Thursday.

Such demonstrations have often been the preserve of Israel's left-wing but this time a surprise beneficiary could be opposition leader Benjamin Netanyahu, a hawkish former prime minister.

His hopes of toppling Olmert have been buoyed by the Lebanon war and concerns over Palestinian Hamas and Iran. The prospect of smoothing the way for a Netanyahu comeback could persuade some liberal protesters to stay at home, cutting crowd numbers.

"The effectiveness of this event all depends on to what extent it is cross-partisan," said Amotz Asa-El, executive editor of the conservative Jerusalem Post.

Asa-El argued the Winograd report could prove to be more effective in generating long-term electoral reform in Israel.

He said the current system, in which voters cast ballots for party lists rather than individual candidates, results in a legislature and executive bent more on self-preservation than on proper representation of the electorate.

Another commentator, Ben Caspit of Maariv, interpreted the Winograd report as condemning apathy within a disaffected Israeli society which he said regards "the stock market as much more important than the situation on the northern border".

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