The Labor Party “must be courageous and join the government in order to help advance [the peace process],” Justice Minister Tzipi Livni (Hatnua) said at a speaking engagement near Haifa this week.

“There’s an opportunity now, and there’s a diplomatic process,” said Livni, who leads Israel’s negotiating team to the US-brokered Israeli-Palestinian peace talks. “That’s why it isn’t enough [for Labor] to make speeches about the need for an agreement.”

If Labor joined the coalition now, the justice minister suggested in comments reported by Israeli television news, then the Jewish Home party on its right-wing edge would be forced out, making way for a more dovish government and a better shot at a peace deal.

The comments marked the peak — thus far — in tensions between Livni and Jewish Home’s chairman, Economy and Trade Minister Naftali Bennett. They also marked the clearest expression yet of former Likud darling and daughter of renowned Irgun activist Eitan Livni’s break from the right.

The ferocity of the spat between Livni and Bennett has led to speculation about the health and future of the coalition, not least from Livni herself and her party colleagues.

Following up on Livni’s call for a reshuffle of the cabinet, Hatnua MK Amram Mitzna, a former Labor leader, told a group of students earlier this week that the lifespan of the current government, of which his party is a member, should be measured “in months, not years.”

Of course, since the current government is Israel’s 33rd in just 65 years, predicting a government’s fall is usually a safe bet.

Even so, the discussions of political collapse may be premature, since what is politically good for Livni, or anyone else pinning outsize hopes on the current peace talks, is not good for Netanyahu, Bennett or even the left to whom Livni’s call was directed.

It’s enough to look at Netanyahu’s position to see how unlikely Livni’s hoped-for scenario is. His choice is simple. He currently heads a coalition that accepts him as its unassailable leader, any possible looming crisis with a politically rehabilitated Liberman notwithstanding. For the settlers of Jewish Home and the hawks of Yisrael Beytenu and Likud, there is no other credible candidate for prime minister. Why would Netanyahu abandon that comfortable spot in favor of a national unity government that includes at least one major partner (Labor’s Shelly Yachimovich) who sees herself as the main challenger to a fourth Netanyahu term?

Why would he drop a coalition partner that has no better option for premier for a partner with a major political interest in weakening and eventually toppling him?

Livni’s gambit is also detached from the hard political math. Netanyahu’s coalition has 68 seats in the 120-seat Knesset. Livni’s Hatnua holds just six of them. In other words, Netanyahu can afford to lose Livni and still retain a thin but probably stable 62-seat majority. And he’d free up two ministries — justice and environment — with which to strengthen the loyalty of his remaining partners and even entice Kadima’s two MKs into the coalition.

Furthermore, if Netanyahu openly pushes for a territorial withdrawal, he would cause a fissure within his own Likud party, a fissure that would be arguably more dangerous for him politically than the breakup of the coalition.

In order to push through any conceivable peace plan, then, Netanyahu will almost certainly face a political reshuffling that will likely be far more complicated and precarious than merely switching out Jewish Home for Labor. His coalition will likely demand a national referendum, and it’s not at all clear he will be able to force even a majority of his own Likud to vote in favor of any territorial withdrawal demanded in the agreement.

In Labor, too, there are forces that are loath to sit at Netanyahu’s right hand as he continues to lead an economically liberal and diplomatically conservative government. Those forces now make up the majority of Labor’s activists, judging by polls that show another likely win for Yachimovich in the Labor’s late-November primaries.

Under her leadership, Labor has increasingly emphasized its “hevrati” — the Hebrew term for “social” — economic and domestic policies, focusing on interventionist economic policy and dovish faith in the Palestinian leadership and the American-brokered peace talks.

Labor is also traumatized by the memory of former party chair Ehud Barak’s decision to drag the party into a unity government with Netanyahu, a decision that broke the party in two and weakened Labor itself at the polls and in the Knesset.

So almost no one — not Likud, not Jewish Home, not the centrist Lapid (who, accurately reading the left-right split among the electorate, has gone out of his way to show he is a closer ally of Bennett and Netanyahu than of the left), not even Labor itself — is keen on Livni’s fantasy of a national-unity government.

These political troubles do not make an Israeli agreement to a future peace deal impossible. Yachimovich has promised over a dozen times in the past year to provide Netanyahu with a “safety net” for any political reshuffling he might attempt in order to push an agreement through the government and Knesset. Majorities in both the Knesset and among the Israeli electorate favor a withdrawal-for-peace deal in principle.

But in the Knesset, as among the electorate, a large majority is deeply skeptical such a deal can be achieved. That skepticism keeps this principled support from expressing itself as a clear political force. Even Labor ran its last election campaign without so much as mentioning the Palestinian issue — not because it doesn’t have a position in principle, but because even its own dovish voters don’t take the possibility of an agreement seriously.

Of course, Livni’s main point — that no peace agreement involving territorial withdrawal could pass in a government that contains Jewish Home — still stands. But why would Netanyahu destabilize his government before such a peace deal becomes a realistic possibility worth sacrificing for?

Israel’s chief peace negotiator has thus embarked on a campaign calling on Israel’s prime minister and opposition leader to sacrifice the existing, stable parliamentary order, and in all likelihood their own political futures, for a theoretical peace deal she has yet to negotiate.

As the saying goes, one should not put the cart before the horse.