While other presidents and prime ministers have been close, the Trump-Netanyahu relationship has no precedent in their countries’ history, veteran diplomats say, encompassing deep parallels in their politics, similar struggles with scandals and outright copycatting in how they denigrate opponents. And the relationship has also benefited Mr. Trump, with Mr. Netanyahu’s policies alienating Jewish Democrats and helping Mr. Trump depict the Republicans as Israel’s only reliable source of unconditional American support.

But the prelude to the April 9 election in Israel could well be their last hurrah together.

Mr. Netanyahu’s defeat is now a serious possibility. His party is trailing that of a popular former army chief, Benny Gantz, in the polls. Even if Mr. Netanyahu wins, he may be unable to form a government because Mr. Gantz has vowed not to enter a coalition with him while he faces indictment. And if Mr. Netanyahu could forge a governing majority, it is likely to be so far right as to complicate or even derail the Trump administration’s long-awaited peace plan to resolve the Israeli-Palestinian conflict.

In the United States, Mr. Netanyahu’s new alliance with a racist Israeli fringe party is already freeing Democrats to denounce him with fewer concerns about Republican blowback. And in a matter of months, the criminal case against Mr. Netanyahu could dislodge him from power once and for all.

For now, however, the administration’s favors keep on coming: Secretary of State Mike Pompeo just announced a stop in Israel on a Middle East swing beginning March 18. The political backup is almost certain to reach its peak a few days later, when Mr. Netanyahu is expected to get an Oval Office meeting, if not a formal White House dinner, during the yearly gathering of Aipac, the powerful pro-Israel lobby.

It’s gotten to the point that analysts tracking the American assistance to Mr. Netanyahu’s campaign have taken to guessing what Mr. Trump might toss his way next: merely more plaudits, or perhaps a meatier bone, like endorsing Republican-sponsored legislation to recognize Israeli sovereignty over the Golan Heights.