WASHINGTON — Prime Minister Benjamin Netanyahu’s victory in this week’s Israeli elections has reverberated through American politics, reinforcing Republican faith in the political wisdom of a hawkish foreign policy, worsening his relationship with President Obama, and energizing liberal critics of Israel’s government. But mostly it has complicated the life of Hillary Rodham Clinton.

As she moves closer to making her campaign for president official, Mrs. Clinton now faces a deepening polarization among Jewish Democrats over Mr. Netanyahu and how the United States should deal with his government.

Mrs. Clinton, the former secretary of state who has long advocated a two-state solution and once took credit for starting what were then secret talks for an Iran nuclear deal that Mr. Netanyahu vehemently opposes, is now likely to be under increased pressure from her own party to speak up against a government that is openly hostile to Mr. Obama. But if she criticizes Israel, she risks prompting an influential segment of more conservative Jewish Democrats to withhold their support from her presidential campaign, or even to defect to a Republican candidate in 2016.

“Everyone is now going to have to pick a side,” said Jeremy Ben-Ami, the president of J Street, a liberal Jewish lobby that has supported Mr. Obama’s positions on Israel and is hosting its annual conference this weekend. That included the woman at “the forefront” of the Democratic Party, he said, who would undergo “more and more pressure.”