Whether it is President Obama today or a successor tomorrow, the President will need to make decisions based on the circumstances of his or her time. That such circumstances were shaped, in part, by decisions made in the past by the U.S., along with external forces many of which are beyond U.S. influence, matters little. They still need to make choices. Sometimes one has to make the least bad choice from among options that are all not very appealing.
As one who falls in the Realist foreign policy camp, my focus would be on limiting American intervention to cases where critical American interests are involved. That would mean focusing on maintaining an open Persian Gulf, assuring that the regional balance of power does not shift in a position to threaten that vital interest, and safeguarding and supporting regional American allies (Israel, Jordan, Egypt), etc. I don't support using military force for democratization projects, as democracy depends far more on internal factors than who heads a country. I don't support military action where there is an absence of critical American interests i.e., I opposed recent U.S. military intervention in Libya and oppose U.S. intervention in Syria's sectarian conflict.
My position differs from that of neoconservatives who believe force can be used to expand the sphere of democracy and liberal internationalists who believe that international law essentially supplants the balance of power/Realpolitik and can be used to liberalize countries. I also do not support to the evolution in liberal internationalist thought concerning the use of force under the notion of a "responsibility to protect." Genocide, consistent with the definition in the Convention on Genocide is a singular exception. Sudan, Syria, Nigeria, etc., do not fit that definition. My position also differs from the neo-isolationist/non-interventionist group, which is built on the assumption that the U.S. essentially has no critical overseas interests and, therefore, should not intervene in international developments.
All of this does not mean that I'm right, nor that my positions should not be criticized, etc. However, that's the context in which I suggest that the U.S. airstrikes against the Islamic State on behalf of the Kurdish Regional government, arms provided to the Kurdish Regional Government are appropriate, and if that government declares sovereignty, the U.S. should support that outcome. The KRG is a friendly government to U.S. interests, has been a reliable partner, it is democratic in nature, though its democracy is not the key factor, and the Islamic State has threatened genocide against the Yazidis.
At the same time, I don't support similar measures on behalf of Baghdad (something advocated by Senator McCain). The Iraqi government headed by Prime Minister Maliki has not been reliable with respect to U.S. interests, has been sectarian not inclusive in nature, which has played a large role in allowing the Islamic State to gain traction in Iraq, and the Prime Minister has called out armed forces to potentially hold onto power, bully Baghdad's other political actors, etc.