Inside and outside Syria, a growing refrain from Mr. Assad’s supporters and opponents alike is that American policy makes little sense — that by trying to avoid taking sides, the United States is neither having its cake nor eating it.

Supporters of Mr. Assad say that the United States should ally with him and his main backer, Iran. They note that Iran’s proxies have already worked indirectly with American-backed forces to fight ISIS in Iraq, and that in Syria, those forces appear far better organized than Mr. Obama’s putative allies, mainstream Syrian insurgents opposed to the Islamic State.

But in Syria, where well over 150,000 people have died in three years of war, such cooperation would put the United States in the awkward position of siding with a government that opponents say has killed many times more Syrians than has the Islamic State. “For years they are killing people, and they didn’t hurt him,” Amjad Hariri, 31, a Syrian refugee in a ramshackle Palestinian refugee camp in Beirut, said of Mr. Assad. “They only went after ISIS.”…

Many of Mr. Assad’s opponents see themselves as stranded between two violent oppressors, the government and the Islamic State. Others who “could have been peeled off,” Mr. Hokayem said, are now embracing the militants as they lose hope of United States action against Mr. Assad, who they see as “a greater threat.”