The Israeli operation in Lebanon is exposing the failures of U.S. efforts to de-escalate the Middle East conflict, raising the likelihood of a full-scale war against Hezbollah and testing President Biden's support for Israel's expanding military campaigns.  Israel has increasingly been a source of stress for the Biden administration throughout the nearly yearlong conflict in the Middle East, as Biden has unsuccessfully pushed Israeli Prime Minister Benjamin Netanyahu to accept a cease-fire and hostage-release deal in Gaza. The widening of the conflict into Lebanon marks a historic act of defiance from Netanyahu and risks stoking an intense regional conflict, a point that was on stunning display Tuesday when Iran fired some 180 ballistic missiles at Israel.  Michael Makovsky, president and CEO of the Jewish Institute for National Security of America, said Netanyahu is purposefully “defying Biden,” in part because he is in a lame-duck session, and Vice President Harris is running for president in a tight race.  “They feel that they can get away with that a little more because ... [Harris] doesn't want to look like she's not being supportive of Israel,” he said.  But Makovsky said Netanyahu’s government also believes the U.S. has been wrong throughout the conflict, including when the Biden administration urged Israeli troops not to enter the southern Gaza city of Rafah over the spring because a million Palestinians were sheltering there at the time.  “I think they realized after the Rafah operation, which was significantly better than expected,” Makovsky said, “that just fundamentally they feel you can’t let the [U.S.] dictate their policy.”  Netanyahu has shown little willingness to cooperate in the Gaza war, even amid domestic and international pressure, much to Biden’s frustration.  Brian Katulis, senior fellow at the Middle East Institute, told The Hill the Biden administration has not achieved many of its goals over the last year because “it's been feckless and reactive to events” in the Middle East.  “We don't have a credible strategy that shapes dynamics. And the real drivers are the ones who are the actors in the region, Israel, Iran, Hamas, Hezbollah, and we're basically just reacting to the plays they've been executing and running,” he said.   Katulis said the Biden team has been unwilling, for several reasons, to exercise sufficient leverage, including diplomatic and security pressure to fundamentally reshape dynamics in the region. He also spoke of a larger declining U.S. influence in the region.  “U.S. leverage and influence has declined and diminished over 25 years,” said Katulis, who pointed to the war in Iraq and the failure to establish peace between Israel and Palestine. "This is a broader crisis, not just related to the Biden administration."    Israel and the U.S. have clashed over everything from the dire humanitarian aid situation in Gaza to reducing civilian casualties in the coastal strip, where more than 41,000 people have died in the past year.  But the cease-fire and hostage-release deal has been the most frequent point of contention. The U.S. has repeatedly said both sides are on the brink of an agreement, only for Netanyahu to pledge to fight on until Hamas is completely defeated. Hamas, too, has often frustrated the talks.  Biden’s frustration with Netanyahu has at times boiled over publicly, including in a notable hot-mic moment earlier this year in which he said that he and the Israeli leader needed a “come-to-Jesus meeting.”  The conflict in Lebanon has also seen aggressive U.S. diplomatic efforts for months, with the American envoy in the region, Amos Hochstein, trying to enforce a United Nations resolution that would see Hezbollah fighters withdraw from the border area.  But Israel, with operations wrapping up in Gaza, has freed up resources and troops, sending them north to begin a larger fight to push back Hezbollah from the border and make way for some 60,000 displaced residents to return home.  The U.S. last week proposed a three-week truce — backed by several countries, including European allies and Saudi Arabia, the United Arab Emirates and Qatar — to temporarily cease hostilities and work on an agreement.  But Netanyahu rejected it — despite the Biden administration claiming Israel was heavily involved in its drafting. He then delivered a fiery speech before the U.N. General Assembly, vowing to continue the fight against both Hamas and Hezbollah.  Behind the scenes, however, some U.S. officials were supportive of Israel’s move into Lebanon, Politico reported this week.  Masoud Mostajabi, deputy director at the Atlantic Council, said the Biden administration has permitted Israel to “move as it sees fit” after the Oct. 7 attacks, despite the public expressions of concern. “Meanwhile, the U.S. will go ahead and provide the means and the political, diplomatic cover on the international stage,” Mostajabi told The Hill.   He added that Israel is confident the U.S. “will side with Israel at the end of the day, when push comes to shove, so it can do what it wants even if that may frustrate Biden.”  Israeli officials have said Hezbollah was planning a major attack, similar to Hamas’s Oct. 7 invasion, during which they killed some 1,200 people in Israel and took some 250 hostages, and that it was necessary to conduct limited operations on the border in Lebanon to clear out fighters and terrorist infrastructure.   But it’s unclear if Israel can quickly achieve a military victory against Hezbollah.  Sean McFate, adjunct professor at Syracuse University, warned that the U.S. will get “sucked into” a further deteriorating situation in Lebanon that will end up harming American credibility in the Middle East and beyond. McFate, a former paratrooper and private military contractor, said Netanyahu’s response, which has been at odds with the Biden administration, “shows that the U.S. is losing leverage.”  “Bibi is essentially ignoring Biden,” he added.  While the U.S. has repeatedly cautioned against a wider military conflict, it has been largely supportive as Israel has done just that.  Israel has decimated Hezbollah’s command structure through airstrikes and savvy attacks, such as one carried out by detonating pagers and handheld radios in Lebanon. U.S. officials said justice was served when the head of Hezbollah, Hassan Nasrallah, was killed last week.  And on Tuesday, Pentagon press secretary Maj. Gen. Pat Ryder said “we fully support Israel's right to defend itself against Hezbollah,” the day after Israel deployed troops across the border into Lebanon.  “As we understand it, they will be conducting limited operations to destroy Hezbollah infrastructure that's arrayed along the border there that could be used to threaten Israeli citizens,” he said. Ryder added the aim was still to “ultimately de-escalate those tensions and get to a cease-fire.”  The support came more than a day after Israel already moved into Lebanon. Retired Brig. Gen. Anthony Tata, a former undersecretary of defense for policy in the Trump administration, said that Netanyahu has likely reached an understanding that the U.S. is not giving him the support he wants politically.  “Netanyahu understands he's got to go this alone,” he said.  Overshadowing the Lebanon war is Iran, which largely failed in its Tuesday missile attack on Israel thanks to the country’s Iron Dome air defenses.  Still, Netanyahu has vowed that Iran will pay for the attack, and a harsh Israeli response could provoke Tehran into responding again.   The spiraling conflict is what the Biden administration has tried to avoid since the Oct. 7 attacks last year.  Katulis of the Middle East Institute advised the U.S. to work more with some of its partners in the region, especially the Arab partners, Jordan, Egypt and Saudi Arabia.   Simone Ledeen, a former deputy assistant secretary of defense for the Middle East in the Trump administration, said the U.S. had lost its sway over Israel, due to what she called the “Biden-Harris policy of appeasement to Iran.” “Israel has stopped referring to the United States the way that it did earlier in the conflict,” said Ledeen.