Though Syria and Israel have technically been at war for more than 40 years, the conflict in Syria is now viewed mainly through the prism of Iran. A prolonged conflict is perceived as hurting Iran, which finances Mr. Assad’s war effort. Whether Mr. Obama follows through on his promise to retaliate for the use of chemical weapons is a test of his commitment, ultimately, to prevent an Iranian nuclear bomb — as long as the retaliation does not become a full-scale intervention in Syria.

“If it’s Iran-first policy, then any diversion to Syria is not fruitful,” said Aluf Benn, editor of the Israeli newspaper Haaretz. “From the Israeli point of view, the worst scenario is mission-creep in Syria and America gets entangled in a third war in the Middle East, which paralyzes its ability to strike Iran and limits Israel’s ability to strike Iran as well.”

This spring, when an Israeli official called for an international response to what he said were earlier Syrian chemical attacks, he was muzzled and reprimanded for appearing to pressure the White House. Now, said Eyal Zisser, a historian at Tel Aviv University who specializes in the region, “it’s clear that Israel does not want to appear as somebody that is pushing the United States for a deep involvement.”

There are significant differences between Israel and the United States on Syria. There was widespread criticism here of Mr. Obama’s decision to delay responding to the chemical attack, with the quote “When you have to shoot, shoot, don’t talk” from “The Good, the Bad and the Ugly” becoming a common refrain. One Israeli dentist even took out a large newspaper ad promoting his implant services with a picture of Mr. Obama captioned, “He doesn’t have teeth?”

There has also been a broader debate about how best to respond to the war in Syria.

When the uprising began, many here saw Mr. Assad, who like his predecessor and father had maintained quiet on the border, as “the devil you know,” and therefore preferable to the rebels, some of whom were aligned with Al Qaeda or Sunni militants like the Palestinian Hamas faction.

As the death toll has mounted, more Israelis joined a camp led by Amos Yadlin, a former head of Israeli military intelligence, who argues that the devil you know is, actually, a devil who should be ousted sooner rather than later.

That split remains. But as hopes have dimmed for the emergence of a moderate, secular rebel force that might forge democratic change and even constructive dialogue with Israel, a third approach has gained traction: Let the bad guys burn themselves out.