NATO is a defense treaty. We wouldn’t be obligated to come to the aid of Turkey. However, the United States does have a treaty with Israel to give aid to her, if attacked. For example, during the first gulf war. Israel was provided Patriot Missile batteries, along with training on how to use them.
And you really think Obama will abide by the terms of our treaty with Israel? He might be blocked from actively taking Turkey's side, but he's guaranteed to ignore any obligations to Israel (at least until it's too late to do Israel any good).