Point taken. His approval numbers do appear to have improved some since their low point just prior to the bombing, however. Whether that was caused by the bombing or not is hard to tell. But I do believe if he dramatically increased American invervention in Syria then his approval ratings would increase substantially.
I'm not so sure. War is somewhat popular -- in the abstract. People like the idea of showing that America is "tough", but they start getting weary once they hear about it on the news every day for months and months. It's what happened with Iraq.
A war only seems to be unpopular when America isn't winning it. Among those of us who're anti-war it'll always be unpopular, but history has shown countless times that we're the minority. The majority of Americans will rally behind a war until they start seeing all the caskets coming home and endless news reports for months of a lack of success in the mission. It's that alone, not even the potentially countless civilian deaths or total destruction of another country, that discourages Americans' support for war.
A war is popular if it's a quick victory like the 1st Gulf War or a sustained national effort against a powerful threatening enemy like World War II. However, these are fairly uncommon nowadays, and long-term quagmires with guerilla warfare, nation-building, and mission creep have been far more common since 1945. Even the Korean War was unpopular at the time.
