For the past three years, figures in America’s foreign policy establishment as well as media kibbitzers who knew little about Israel had a constant refrain: Tzipi Livni, the glamorous head of the Kadmia Party, should replace Benjamin Netanyahu as Israel’s prime minister. In the aftermath of Netanyahu’s election in February 2009, the Obama administration openly plotted to topple the new leader and replace him with Livni, whom they viewed as more pliable on the Palestinian issue. Once that ploy failed as President Obama’s attacks on Netanyahu only strengthened him at home, Netanyahu’s American critics could only sit back and wait patiently until Livni defeated him on her own. But the wait is going to be a lot longer than many in Washington thought.

Last night, Livni lost her perch as opposition leader as the members of her rapidly shrinking party rejected her in favor of former General Shaul Mofaz in a primary to determine who will top the party’s list in the next election that is currently scheduled for October 2013. That Livni, who was feted abroad and was prominently placed on lists of the world’s most important women, was defeated at all will come as a shock to her foreign admirers. But this was no ordinary defeat. The lady who only a couple of weeks ago was lauded as Israel’s “voice of reason” in a fawning piece by John Avlon in the Daily Beast, was slaughtered by Mofaz, 62-38 percent. The question now is whether Americans who were under the delusion that Livni represented a viable alternative to Netanyahu’s popular government will get the message.

The Kadima that Mofaz will lead into the next election is vastly diminished from the juggernaut formed by Ariel Sharon when he left Likud in the wake of the withdrawal from Gaza in 2005. Sharon skimmed the biggest opportunists in Labor and Likud to create what many imagined to be the first viable centrist political grouping in the country’s history. But after its bigger-than-life leader was removed from the scene by a stroke, Kadima was seen to be an empty shell whose only purpose was to find government posts for its leading personalities. Ehud Olmert led it to an election victory in 2006 in the immediate aftermath of Sharon’s illness but was soon proved to be hopelessly over his head.

Livni served as his foreign minister and hoped to replace him after the disastrous Lebanon war but was outmaneuvered by Olmert. That was an early sign she had no capacity for leadership. She got her chance to run for prime minister in 2009. As a fresh face with no corruption charges currently pending against her, Livni ran a good campaign and enabled Kadima to win the most seats. However Netanyahu’s coalition of center-right parties far eclipsed its total. But rather than serve under another rival, she made the fatal mistake of leading Kadima into the opposition. The problem was that Livni and Kadima lacked any coherent vision of a different approach to Israel’s problems. Though Americans who disliked Netanyahu saw her as the pro-peace alternative, Israelis were aware her views on the issues were almost indistinguishable from those of the Likud leader. Her only real disagreement with him was based in her conviction that she ought to be Israel’s prime minister, a point on which few of her countrymen, even the members of her own party, agreed.

Some Israeli pundits think the selection of Mofaz is a blow to Netanyahu, as he was obviously relishing a chance to trounce her at the polls. But the former general will be another disappointment to American Bibi-haters. The gruff former military man won’t win the hearts of Westerners longing for a weak Israeli leader. He will try to carve out a position slightly to the left of Netanyahu, but Israelis understand the Palestinians have no interest in negotiating a two-state solution under any terms they can live with. Though he may prevent Kadima from collapsing at the next ballot, the party is facing stiff competition from a newly revived Labor and another new centrist party led by Yair Lapid. Polls show that none have a ghost’s chance of beating Netanyahu and Likud.

Livni will, no doubt, have a successful career ahead of her speaking to liberal American Jewish groups for large speaking fees much as her former boss Olmert got cheers at the J Street conference last week that the former PM, who is a pariah in Israel, could never hope to get at home. But the lesson here is that Israelis who are more popular in Washington than in Jerusalem and Tel Aviv are not to be taken seriously.