The brief statement included the diplomatic essentials. Israeli Prime Minister Netanyahu “congratulates President Barack Obama on his election victory” and notes that the strategic alliance between the two countries is “stronger than ever.”

What it didn’t convey was the not-so-diplomatic truth about Netanyahu and the American presidential race: that the Israeli leader preferred Obama’s rival, Mitt Romney, and did a poor job of hiding it in the months leading up to yesterday’s vote.

Now, as Obama sets his agenda for the next four years, some Israelis believe he will return the favor by taking tougher positions with Netanyahu on things like negotiations with the Palestinians.

Others wonder if Obama might even try to subtly undermine Netanyahu’s reelection campaign. “Netanyahu took a huge risk, one that no other prime minister has ever dared take. He bet on one of the candidates in the American presidential campaign,” said Raviv Drucker, a political analyst for Israel’s Channel 10 News. “But the gamble failed and now he has to contend with the results,” he told Israel’s Army Radio.

Netanyahu, whose relationship with Obama has been fraught since their first summit meeting in 2009, denies having taken sides. Some members of his ruling coalition rushed to make clear they’re not disappointed by Obama’s victory.

“I think he’ll be a very good president for Israel,” said Danny Ayalon, the deputy foreign minister.

But others said quietly that on everything from settlement expansion in the West Bank to military action against Iran’s nuclear program, Romney, the Republican candidate, would have allowed Netanyahu more leeway. The assumption stems in part from the campaign rhetoric of Romney himself, who accused Obama during the campaign of being too harsh with Netanyahu and “throwing Israel under the bus.”

But it also reflected a higher comfort level Netanyahu and other members of his right-wing government have with Republicans over Democrats. “We hope to see a change in Obama’s attitudes towards Israel,” Likud lawmaker Danny Danon said about his reelection. “A change that shows he understands that he cannot appease the Muslim world and pressure Israel,” he told The Daily Beast.

Officials close to Netanyahu have said he laments that his two terms as prime minister have coincided with Democratic presidencies. Netanyahu first served as Israel’s leader from 1996 to 1999, while Bill Clinton was in the White House. He faced heavy pressure from Clinton to accept compromises with the Palestinians stemming from the Oslo peace accords. One Washington insider said Obama-administration people refer to Netanyahu lightheartedly as the “Republican representative from the state of Israel."

Obama supporters point to Netanyahu’s embrace of Romney during the candidate’s visit to Israel in August and his harsh criticism of Obama in September over his handling of the nuclear crisis with Iran as examples of Netanyahu’s unseemly involvement in the race.

The Israeli newspaper widely viewed as a mouthpiece for Netanyahu’s Likud party, Israel Hayom, ran no fewer than four opinion pieces on Tuesday endorsing Romney. While the arguments for backing Romney resonated with many Israelis, they seemed to have little impact on American Jews. Exit polls showed some 70 percent of Jewish voters cast their ballots for Obama, only slightly less than in 2008.

Drucker, the political analyst, said Obama’s posture ahead of Israel’s Jan. 22 election depended on the country’s political landscape. “Obama will ask himself whether there’s a real rival to Netanyahu in the Israeli election campaign. If he sees one, it could be that in a very subtle, very polite way, he might try to help the rival.”

He said it would be enough for Obama to invite an opponent of Netanyahu’s for a meeting in Washington ahead of the election in order to signal to Israelis voters which candidate the U.S. favors.

Most polls show Netanyahu winning the election and governing for another four years with roughly the same coalition of right-wing and religious parties he presides over now. The picture could change if Ehud Olmert, a former prime minister and political centrist, enters the contest. Analysts believe Obama’s victory raises the chances of Olmert joining the race.