With word that Tzipi Livni, former foreign minister and leader of Hatnuah (התנועה, ‘The Movement’), will become the first major figure to join prime minister Benjamin Netanyahu’s governing coalition for a third term in office, nearly a month after Israel’s legislative elections, we’ve reached a new critical phase of the coalition-building process.

Livni will not only serve as justice minister in the new government, according to the agreement with Netanyahu, but will also be the government’s exclusive negotiator for any peace talks with the Palestinians.  Her party, Hatnuah, will also receive another cabinet position, most likely environmental protection.

Netanyahu has until mid-March to form a government, six weeks from the date when Israeli president Shimon Peres invited him to form a coalition.  Although Netanyahu may be granted a 14-day extension, the pressure is now on to form a broad-based government, even though Netanyahu’s own Likud (הַלִּכּוּד‎, ‘The Consolidation’) holds just 20 seats in the Knesset (הכנסת), Israel’s 120-member unicameral parliament.

With his electoral coalition partners, the secular nationalist Yisrael Beiteinu (ישראל ביתנו‎, ‘Israel is Our Home’) of former foreign minister Avigdor Lieberman, ‘Likud-Beiteinu’ holds 31 seats, so even the merged coalition is likely to be a minority within the larger governing coalition.

Hatnuah, which includes Amir Peretz, former leader of the Labor Party (מפלגת העבודה הישראלית), and defense minister from 2006 to 2007, and Amram Mitzna, also briefly a former leader of Labor (from 2002 to 2003) and former mayor of Haifa, won only six seats in the election, so Netanyahu has a long way to go. But by bringing Hatnuah into the fold, and by giving it two portfolios,‡ Netanyahu is signaling that it’s more important to have Livni within government than outside it.

It’s somewhat surprising to see Hatnuah become the first party to join forces with Netanyahu after January’s elections, given Livni’s steadfast opposition to joining a Netanyahu-led coalition four years ago.

Livni led the centrist Kadima (קדימה, ‘Forward’) in the previous 2009 elections, and she managed to win 28 seats to just 27 for Likud.  Livni, however, couldn’t find enough partners to form a coalition and when she refused to join Netanyahu’s coalition, Netanyahu found more willing allies in Lieberman and former prime minister Ehud Barak, then the leader of Labor.

Kadima, in opposition for three years and declining in the polls, dumped Livni as leader in March 2012.  She promptly resigned from the Knesset, only to return to politics in advance of the 2013 elections with her new party, Hatnuah.

So where does the Netanyahu coalition go from here?

Here are four things that the Livni-Netanyahu alliance signals to us about the next Israeli government:

1. The care and feeding of the United States will be important in Netanyahu’s third term.

With U.S. president Barack Obama planning a trip to Israel in March, there’s a sense that Netanyahu is taking a more deferent tone to the U.S. administration than he did during Obama’s first term — after publicly calling on Obama to name ‘red lines’ with respect to the Iranian nuclear program last year, Netanyahu is now christening the March visit ‘Operation Enduring Alliance.’ Nothing subtle about that.  Netanyahu knows that he’ll have to work with Obama for the next four years on all sorts of tricky issues, Iran’s nuclear weapons program being only the most pressing of them.

Livni is one of the most dovish politicians in Israel, one of the few remaining figures that still earnestly believes in the Palestinian peace process.  By naming her early to his cabinet and by indicating that she will have such a central role in any Israeli-Palestinian negotiations, Netanyahu is reassuring the United States and Europe that there will be moderates in his government, and Livni may well take Barak’s place in the upcoming government as the Americans’ favorite minister.

Although Barak, who had served as defense minister since 2007, declined to run in the recent elections, there’s been some talk that he might stay on as a non-MK defense minister or even as Israel’s ambassador to the United States — retaining both Barak and Livni in high-profile roles would be most welcome by the Obama administration.

2. Netanyahu wants to rupture the new odd-bedfellows alliance between Yair Lapid and Naftali Bennett.

After last month’s Knesset elections, it was clear that Yair Lapid‘s new centrist party, Yesh Atid (יש עתיד, ‘There is a Future’) was the big winner with 19 MKs, making it the second largest party in the Knesset.  It seemed even clearer that Lapid would be joining Netanyahu’s coalition, perhaps even as finance minister or foreign minister.  But thereafter, talks stalled over whether the haredi parties (Shas and United Torah Judaism) would join the coalition as well — longtime allies of Likud, the ultraorthodox parties are at opposite ends with Lapid, who wants to end any special exemption for yeshiva religious students from national service.

In recent days, however, Lapid has joined an alliance with Naftali Bennett, whose Zionist right-wing Bayit Yehudi (הבית היהודי, ‘The Jewish Home’), which is even more to the right that Likud-Beitenu, also made gains in the elections, winning 12 seats.  Lapid and Bennett have informed Netanyahu that they will either join the coalition together or not at all.  In part, that’s because they see relatively eye-to-eye on national service.  In part, it’s because of the awkward personal dynamics between Netanyahu and Bennett, who once served as Netanyahu’s chief of staff from 2006 to 2008 and who has tangled in the past with Sara Netanyahu, the prime minister’s wife.

Mostly, though, Bennett-Lapid alliance seems like a really smart power play, and it has certainly made things more difficult for Netanyahu.

Consider the current coalition math: with Hatnuah, Netanyahu has only a 37-MK coalition.  He needs to bring with him at least two of the following four groups: the two haredi parties (18 MKs), Yesh Atid (19 MKs), Bayit Yehudi (12 MKs) or Labor (15 MKs).

Netanyahu wants to include the haredi parties because they’ve been strong allies in the past, but Lapid is opposed to a coalition that includes them.  While Bennett agrees with Lapid on the national service issue, Bayit Yehudi sat in government with Netanyahu and the haredi parties in the last Knesset.  But so long as Bennett refuses to join a coalition without Lapid, the haredi parties seem likely to be excluded.  Netanyahu could pull a runaround with a Labor-haredi coalition — that seems unlikely but not impossible.  (More on that below).

So while the Lapid-Bennett alliance holds, they can together demand much more than either one could demand separately.

Bringing Hatnuah into the coalition, however, draws out the ideological tensions between Bennett, whose pro-settlement view couldn’t be more at odds with Livni’s approach to the Palestinian issue, and Lapid, who will find in Livni another moderate voice in the government.  Although Bennett says that his party could join a coalition with Livni, Netanyahu’s gambit is in part a maneuver to divide Lapid and Bennett a little further.

3. Avigdor Lieberman’s heyday is over — and the next Netanyahu government will be marginally more amenable to Palestinian peace negotiations.

Netanyahu has good reason to rue his electoral alliance with Yisrael Beitenu.  Although the merged bloc won 31 seats, that’s fewer than the combined 42 seats they held in the prior Knesset.  The 20 seats that are allotted to Likud members are certainly fewer than Likud would have won if it had instead contested January’s elections without Yisrael Beitenu.

Meanwhile, Lieberman, who previously served as foreign minister, is on trial for fraud and breach of trust stemming from a longtime corruption case.  Although acquitted of most charges late in 2012, prosecutors have appealed these charges, meaning that Lieberman will be busy fighting legal challenges throughout the spring.

Netanyahu has expressed hope that, upon a new Lieberman acquittal, he could rejoin Netanyahu’s cabinet as foreign minister and has indicated he will hold open the portfolio for Lieberman, pending outcome of the trial.  But some MKs have already called for Lieberman to move to finance, with Lapid or someone else taking over the foreign ministry.

By granting Livni such wide berth for conducting negotiations on behalf of the Israeli government with the Palestinian government, Netanyahu has already undermined Lieberman’s authority, if and when he returns as foreign minister.

It’s not certain that there will be any chance for Livni to negotiate, given that Palestinians have demanded that Israel halt construction of new settlements as a condition for future talks.  But Netanyahu has expressed more optimism over peace talks in his next government, and naming Livni to such a high-profile role is a hopeful sign for the pro-peace camp and an ominous sign for hardliners like Lieberman and Bennett.

Lapid’s likely presence in government will also pull Netanyahu in the direction of peace talks, though while he’s more pro-peace than Lieberman, he’s hardly a dove when it comes to the Palestinian issue.  Moreover, as Jeffrey Goldberg noted last week, however, a government marginally more interested in talks doesn’t mean we should start betting on a two-state solution anytime soon.

4. It’s still more likely than not that Labor leader Shelly Yacimovich will remain the chief opposition leader.

Yacimovich was the most prominent voice for greater economic equality and opportunity during the election.  Although Lapid falls somewhat to the left of Netanyahu, Livni and Bennett on economic issues, the next government seems certain to cut Israel’s budget to reassure bondholders, which means the government-backed spending on education and economic opportunity that Yacimovich favors will not be part of the agenda anytime soon.

In addition, Yacimovich was quite clear about her refusal to join any Netanyahu-led coalition during the campaign.  Although those kinds of promises aren’t worth much in Israeli politics, they are a bit more credible with Yacimovich.  Under her leadership, Labor has remained in opposition — in contrast to Barak, when he led labor, or Kadima’s current leader Shaul Mofaz, who briefly joined Netanyahu’s government in summer 2012.  With Livni now joining Netanyahu’s next government, and Lapid also likely to join it, Yacimovich would be the only consistent Netanyahu opponent who could conceivably win the next election.

There are rumors that Netanyahu has offered Yacimovich the finance ministry in his next government, however, which would mean a U-turn for Netanyahu on economic policy.  That wouldn’t be unheard of in Israeli politics, either, but it’s still just a rumor.  As noted above, with Yacimovich and the haredi parties in government, Netanyahu would have a majority without Lapid and Bennett.  Bringing Labor into the coalition would be an instance of Netanyahu placing political flexibility above any particular commitment to policy positions.

It still seems more likely that Lapid and Bennett will ultimately join the government.  In that scenario, Lapid will be inexorably tied to the government’s budget policies in advance of the next election — even more so if he’s appointed finance minister.  It’s doubtful that, by 2017, Lapid could recapture the energy that brought him such electoral success in January’s elections, and Yacimovich stands most to gain from those efforts.

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‡ Incidentally, one of the subplots of the latest move is whether Mitzna or Peretz will serve as the second Hatnuah government minister, which highlights how tenuous party affiliations remain in Israel, and how much coalition-building depends on personalities and portfolios.