(CNN) -- For months, Republicans derisively doubted if U.S. President Barack Obama was a true friend of Israel and Prime Minister Benjamin Netanyahu, questioning if Americans should re-elect someone who might not be on the same page with the long-time U.S. ally.
Now, it's Netanyahu facing political heat in his own country -- for his relationship with Obama.
Despite sometimes blistering attacks over where his administration stands on Israel and against Iran's nuclear program, Obama this week emerged victorious in the U.S. presidential election. But Netanyahu has months to go in his own campaign, including time to answer questions about his relationship with the American leader.
Leading the charge against the prime minister is the Kadima party, which holds more seats at 28 than any other in Israel's Knesset and which quit Netanyahu's coalition government in July. The centrist party is among those aiming to gain more power and unseat Netanyahu when Israelis go to the polls on January 22, 2013.
Kadima wasted little time after Obama's election win in going after Netanyahu. In a post Wednesday on its Facebook page, the party claimed the prime minister had sided with U.S. Republican presidential nominee Mitt Romney and could not be trusted -- by Obama and, moreover, by Israelis -- to be a robust, effective partner with Washington. In that post and in an open letter on its website, Kadima highlighted the importance of U.S.-Israeli relations.
Jewish media is abuzz, too, about a Wednesday speech by former Prime Minister Ehud Olmert in which he claimed that Netanyahu had interjected himself into the U.S. election by trying to undermine the incumbent president. Multiple Jewish media outlets reported Olmert said Netanyahu got involved in part to satisfy Sheldon Adelson, who donated close to $100 million this year toward defeating Obama and electing Republicans to Congress, according to insiders involved in the process.
The Jerusalem Post reported Olmert said that "Netanyahu's behavior in recent months brings up the question if Netanyahu has a friend in the White House, and I'm not sure."
"This represents a significant breach of the basic rules governing ties between nations, made worse by the fact that these are allies like Israel and the United States," Olmert said in the same speech to Jewish leaders in New York, according to another leading Jewish newspaper, Haaretz.
Netanyahu and officials in his government have beaten down such accusations of meddling, while playing up what they describe as strong ties between Israel and the United States.
In a statement congratulating Obama, Netanyahu said, "The security relationship between the United States and Israel is rock solid, and I look forward to working with President Obama to further strengthen this relationship."
In an interview Thursday with CNN's Christiane Amanpour, Deputy Foreign Minister Danny Ayalon acknowledged that Romney and Netanyahu have a special connection from having once worked together at the same U.S.-based consulting firm, but "to say there was a preference, it's a little bit of a stretch."
"We have no better friend than President Obama," Ayalon said, repeating an assertion he'd made previously.
The deputy foreign minister credited Obama with spearheading international sanctions and other punitive measures that he said has made Iran "very vulnerable ... socially, politically, economically." Whatever past differences there might have been about timelines and goals, Ayalon said Israel will follow the U.S. president's cue when it comes to Iran.
"I think today we can safely say that we are very much of the same page, and we'll continue to follow the lead of the United States," he said.
Such a line of questioning, and political attacks, about U.S.-Israeli relations is nothing new -- as evidenced in the recent U.S. election.
For months, Republicans hammered Obama, claiming he hadn't been a loyal enough friend to Netanyahu or tough enough on Iran.
One public dust-up came earlier this fall, when Israeli sources told CNN the White House had turned down a request for a meeting between Netanyahu and Obama while both were in New York for a U.N. meeting, prompting Romney to say he "can't imagine ever saying no" to a meeting request from Netanyahu. The White House later said no request had been made, and within hours of the story breaking, Obama called the prime minister and said the two countries maintain "close cooperation on Iran and other security issues."
The Obama administration has stressed repeatedly that it is committed to maintaining a strong relationship with Israel. In May 2011, the president said, "The bonds between the United States and Israel are unbreakable, and the commitment of the United States to the security of Israel is ironclad."
Now, the same issue -- how well can Netanyahu and Obama work with and trust each other -- is being debated nearly 6,000 miles from Washington in another heated election. This is a testament to the unique, historically tight relations between these two nations, as well as the vibrant brand of democracy that define their political systems.
Despite obvious differences, Netanyahu and Kadima leader Shaul Mofaz did unite this week on one matter -- lauding the U.S. political system and expressing their desire for Israel to follow its lead.
Mofaz described "American democracy (as) a beacon for Israel and her people."
Netanyahu, meanwhile, characterized the United States as "the greatest democracy on Earth."