The debate over whether to bomb Syrian military facilities and weapons installations is creating some strange bedfellows. Among them: President Obama and Las Vegas casino mogul Sheldon Adelson. On Tuesday, the Republican Jewish Coalition, which counts Adelson as a donor and a board member, told its members to urge Congress to authorize a strike in Syria. A spokesman for Adelson, a top backer of pro-Israel causes, told Bloomberg News that the gambling mogul supported the coalition's position—and thus Obama's—on Syria. Obama and Adelson are far from ideological allies. Adelson reportedly spent upwards of $150 million, in disclosed and dark money,...