First of all, war is profitable for the US. They are far from Europe and can use it for their own purposes - the military industrial complex (MIC) supports the US economy. Moreover, Washington finds that it is advantageous to restructure the greater Middle East to their needs. Stepping in at the last stage (as was the case in the WWII), the United States will qualify for the role of one of the winners, regardless of the outcome of the war. A number of political forces (neo-conservatives, the liberal interventionists, pro-Israel lobby) in the United States are actively trying to exploit this issue.
War, under the auspices of NATO, is a danger for Russia. However the possibility of this is also not clear. Several European countries will not support Turkey's request for assistance. In particular, Greece will come on the side of Russia. Previously, Turkey has repeatedly violated Greek airspace. In 2014 alone, Turkey was documented violating Greek sovereign airspace 2244 times. In addition, EU Member States have their own reasons to punish Turkey for the influx of migrants to Europe which passed through its territory. Therefore, even a discussion within NATO about supporting Turkey will create friction between members of the alliance.