The president has won bipartisan plaudits for his response to the war, and his trip to Israel offers a chance to appear statesmanlike. But anger on the left is growing as Israeli strikes pound Gaza.As President Biden visits Tel Aviv on Wednesday to demonstrate American solidarity with Israel amid escalating violence after the deadliest attack it has faced in 50 years, Democratic rifts over the conflict are beginning to tear open, leaving him presiding over a party struggling to resolve where it stands.The president’s trip, and his broader handling of the war, have presented him with both political risks and a chance to pump energy into a re-election bid that Democratic voters have been slow to embrace.Mr. Biden’s steadfast support for Israel after the Hamas attack, by far the dominant position in Washington, has won him plaudits from some Republicans as well as Democrats. An international crisis, even with its grave geopolitical dangers, is relatively comfortable political terrain for a president with deep foreign policy experience.While international issues rarely drive American elections, Mr. Biden and his allies will see playing the role of statesman abroad — especially if he can help calm the soaring tensions — as a welcome change from a wide range of domestic challenges dragging down his approval ratings.In Tel Aviv, Mr. Biden again offered a full endorsement of Israel while making his most explicit warning yet to its leaders, telling them not to be “consumed” by rage after the Hamas attack. For the first time, the president offered money for displaced Palestinians and cautioned that the United States made mistakes responding to the Sept. 11, 2001, attacks that Israel should not repeat.At the same time, creeping anger within his party’s left is threatening to grow as Israel pummels Gaza with airstrikes and moves toward a potential ground invasion, with progressive Democrats accusing Mr. Biden of abetting a war that has already killed thousands of Palestinians.Those emotions flared on Tuesday after a deadly explosion at a Gaza City hospital, with Israeli and Gazan officials blaming each other for the blast. Protests erupted across the Middle East, a planned stop by Mr. Biden in Jordan was canceled and American politicians rushed to criticize the president even before the fog of war had settled.An Israeli soldier near Urim, Israel, on Tuesday. The country’s military is preparing for a potential ground invasion of Gaza.Tamir Kalifa for The New York TimesThe anger and confusion made clear just how precarious of a tightrope Mr. Biden is walking.“This is delicate for him,” said Representative Jasmine Crockett of Texas, a progressive Democrat who visited Israel with a congressional delegation this summer. “It’s a very fine line to walk and it’s one that a lot of us as members, especially progressive members, find ourselves having to try to balance.”While Republicans who have offered surprising praise for Mr. Biden’s response to the Hamas attack have largely cast the conflict as a black-and-white issue, things are more complicated among the progressive base of the Democratic Party.Large segments of Democratic voters, especially younger ones, are skeptical if not hostile to Israeli policy toward the Palestinians and are disinclined to support a war, even in response to a Hamas attack that killed more than 1,400 Israelis.The discontent has been evident in two documents in recent days. The first, a letter signed by 55 progressive members of Congress on Friday, called for the restoration of food, water, fuel and other supplies Israel had cut off to Gaza. Another, a House resolution with just 13 Democrats as co-authors, demanded “an immediate de-escalation and cease-fire in Israel and occupied Palestine.”Representative Mark Pocan of Wisconsin, who signed the letter but not the cease-fire resolution, said he had received more calls from constituents in his Madison-based district who were worried about Israel’s expected military response to the Hamas attack than about the initial assault itself.Mr. Pocan said he had explained to people that Mr. Biden and his top aides, including Secretary of State Antony J. Blinken, were privately pressing Israel to do more to spare Palestinian lives than they were expressing in public.“We ask people to kind of trust some of us who are saying and doing the right thing,” Mr. Pocan said in an interview on Tuesday. “I know how Joe Biden operates. He’s probably saying some things privately that are important and respectful of civilians. He may not broadcast everything on his sleeve. People just have to understand that that’s Joe Biden. He’s not encouraging the indiscriminate bombing.”But some Democrats warned that if Mr. Biden tethers himself too closely to Israel, he will get blamed if many of the party’s voters come to believe that Israel responded to Hamas with too much force.Representative Rashida Tlaib of Michigan, the only Palestinian American in Congress, who was one of the 13 Democrats who signed the cease-fire resolution, was among the first in her party to blame Mr. Biden directly for war deaths after the Gaza hospital explosion.“This is what happens when you refuse to facilitate a ceasefire & help de-escalate,” she wrote on social media Tuesday. “Your war and destruction only approach has opened my eyes and many Palestinian Americans and Muslims Americans like me. We will remember where you stood.”Mark Mellman, the founder and president of Democratic Majority for Israel, dismissed the idea that Mr. Biden was risking a crackup in his electoral coalition. If anything, Mr. Mellman said, Mr. Biden was demonstrating his dynamism to voters who have questioned his age and ability to serve in office.“It shows a level of vigor, it shows a level of engagement,” he said. “It demonstrates unparalleled diplomatic competence.”Polls show that Americans are more confident in Mr. Biden’s ability to lead the country through the Israel conflict than on domestic issues.Kenny Holston/The New York TimesWhile Mr. Biden’s re-election campaign has not yet sent fund-raising appeals based on his actions in response to the Israel conflict, the pageantry of his trip won’t be lost on officials at the operation’s headquarters in Delaware. After Mr. Biden visited Ukraine, his campaign produced a gauzy advertisement titled “War Zone.”The White House believes Mr. Biden is acting with broad support from the American people in defending Israel. Officials think that those protesting Mr. Biden’s position are not representative of much of the electorate — and that Democrats are hardly likely to abandon Mr. Biden if it means helping former President Donald J. Trump.While Mr. Biden, in an interview on CBS’s “60 Minutes” on Sunday, agreed with Israel’s aim of eradicating Hamas, he said the group was not representative of the Palestinian people. Mr. Blinken said on Tuesday that the United States and Israel had agreed to a plan to enable humanitarian aid to reach Gazan civilians.“It is critical that aid begin flowing into Gaza as soon as possible,” Mr. Blinken said.Among progressives, there is some hope that Mr. Biden’s trip to Israel will serve to de-escalate the conflict just as it appears poised to explode.Larry Cohen, the chairman of Our Revolution, a left-wing political organization that grew from Senator Bernie Sanders’s presidential campaign, said he hoped the visit would do so.“In this moment, the U.S. role potentially helps Palestinians as well,” said Mr. Cohen, whose work in the region dates to a meeting with Yasir Arafat three decades ago to help support workers trying to organize a union in the West Bank. “I believe that Biden is going there in part to try to stop a slaughter in Gaza as well as to express horror at the Hamas murders.”Polls show Americans are more confident in Mr. Biden’s ability to lead the country through the Israel conflict than on domestic issues.A Quinnipiac University poll released Tuesday found that 76 percent of voters thought supporting Israel was in the U.S. national interest. The survey found that 42 percent approved of Mr. Biden’s handling of the Israel conflict, compared with 37 percent who disapproved — an improvement on his overall approval rating, which the poll found was 38 percent.Younger and more activist progressive Democrats seem less inclined to give Mr. Biden the benefit of the doubt. Quinnipiac found that a majority of voters 18 to 34 years old were opposed to sending weapons and military equipment to Israel.Waleed Shahid, a strategist who used to work for Justice Democrats, a group that sponsored left-wing primary challenges to Democratic members of Congress, said Mr. Biden’s embrace of Israel might drive young Muslim and progressive voters away from Mr. Biden and toward Cornel West, the independent candidate for president who is running on a more explicitly antiwar platform.“I have heard from several people in my life, people who worked for Biden in 2020, Jews and Arabs, who just from an ethical perspective don’t feel great about returning to campaign for him,” Mr. Shahid said.On Tuesday in Arizona, Vice President Kamala Harris was greeted with jeers from college students after delivering the Biden administration’s talking points about how both Israelis and Palestinians “deserve peace, deserve self-determination and deserve safety.”One student yelled, “Stop making bombs.”Ruth Igielnik More