Tel Aviv — Politicians in back rooms and pundits on TV were trying Thursday to imagine what Israel's next government might look like. After an election that saw no party win a clear majority, this phase — full of promises and deal-making — sees the parties trying to build a coalition to form a new government.

It was during this part of the process when it all fell apart the last time. That was only about four months ago.

With his political survival on the line, Prime Minister Benjamin Netanyahu is calling for a "unity" government.

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"During the elections I called for the establishment of the right-wing government," he said in Hebrew in a videotaped message posted online Thursday. "But unfortunately, the results… show that is not possible. Therefore, there is no choice but to form a broad unity government."

It was not the definitive outcome Netanyahu hoped for. Voters went to the polls Tuesday in a do-over parliamentary election. But the two main parties, Netanyahu's Likud and chief rival Benny Gantz's Blue and White, virtually tied for the number of seats they picked up in Israel's parliament, or Knesset.

With no clear winner and no one party gaining enough seats to form a government on its own, they are forced to wrangle to try and form a coalition.

Contradictory interests

Coalition building means one-time political foes may have to join forces, and that's easier said than done.

"Their interests are so contradictory," political analyst Barak Ravid, from Israel's Channel 13, told CBS News on the eve of the election. "It's hard to see how such a unity government might be formed."

Gantz has insisted in the past that a unity government with the Likud Party would be possible, but not with Netanyahu at the top. On Thursday, he said again he was open to a coalition, provided he becomes the new prime minister.

Incumbent Netanyahu is facing a possible indictment in a corruption scandal, but would like to keep the top spot. He also wants a majority in parliament, which could grant him immunity from any possible charges.

"This is about personal survival (for Netanyahu)," Ravid told CBS News. He's facing jail time… (and) Netanyahu understands that the only way to get a 'get out of jail free' card is to have at least 61 members of Knesset majority."

Ties to the United States

Netanyahu campaigned big on his ties to the U.S., and to President Trump personally. Huge billboards in Israel show Netanyahu with world leaders, including Mr. Trump. The message to voters was that no one else has those relationships, and Likud campaigned that Israel needed Netanyahu for its very survival.

"He is the one who can do something for us," one supporter told CBS News at a Likud pep rally for supporters on the eve of the election.

But Gantz has argued all along, and he told CBS News directly at an event ahead of the April election, that the relationship between the two countries is more important than any between individuals, and strong enough to endure.

"We are friends of Israel," Mr. Trump said recently, not mentioning any of the close ally's politicians by name.

Trump cooling to Netanyahu?

"In the previous election, President Trump gave Netanyahu a lot of gifts along the way," Barak Ravid told CBS News, referring to the recognition of the Golan Heights just ahead of the April election. Moving the U.S. Embassy from Tel Aviv to Jerusalem was another big policy win for Netanyahu, which was touted during the campaign.

CBS News correspondent Seth Doane, left, speaks with Israeli political analyst Barak Ravid in the Channel 13 newsroom in Tel Aviv, September 2019. CBS

But Ravid suggested that warmth may have cooled in this re-do election.

"It's also clear Trump wants Netanyahu to win, but let's say he made less efforts to show that," Ravid said.

The sweeping gestures and political "gifts" that abounded ahead of the April vote were not there this time around. When Netanyahu announced his willingness to annex land claimed by the Palestinians just ahead of the vote, the Trump administration responded with no change in policy.

Following the vote in Israel, President Trump said he had not spoken with Netanyahu.

Regarding the too-close-to-call results, he said: "We'll see what happens."

A third election?

"Maybe in five months from now we'll be voting again!" voter Omer Eliyahu exclaimed to CBS News at a Tel Aviv polling station on election day.

But many Israelis don't want to see a third, expensive election — and even more political uncertainty.

Israel's president, elected by the Knesset, is responsible for giving a party the mandate to try to form a government.

"It was a surprise last time," Raanan Kessel, a voter at a Tel Aviv polling station told CBS News on election day. "(Israel's) President was surprised, politicians were surprised," he said about the deadlock after the last vote in the spring.

"Not this time," Kessel added, "They'll make some coalition."