As political instability grows in Iraq, there are 3 major concerns from an American Perspective:
- difficulty in clobbering together a credible Iraqi force to defeat Islamic State (IS),
- continued increase of Iranian influence in Iraqi matters and
- loss of global leverage for America's reach in foreign lands.
The first concern is obvious. Obama Administration and Pentagon have been hoping to eject IS from Mosul for last few months. That is not going to happen if Iraqi politics is unstable and as a result her forces are ill-prepared. Americans for right reasons do not want defeat of IS in Mosul entirely as the Kurdish victory story. Ethnic composition of Mosul is such that non-Kurdish Sunni needs to be in the mix of post IS rule in Mosul. That cannot happen as long as the Baghdad government is weak and incapable of putting together necessary resources on the ground.
In a sense Saudi drive to pull down global oil price as a way to contain post nuke accord Iran is costing Iraqi PM Abadi mighty. As a rentier state, Baghdad gets most of its money by selling Oil. As Abadi is not able to get enough petro-dollars; his writ gets challenged. I guess part of the solution for Obama Administration will be simply 'wait out' hoping climbing Oil prices will help Abadi. Sure, NeoCons are all going to blame Obama no matter what.  But America simply does not have the choice of putting American soldiers back in Iraq. There is no way American soldiers are going to fight battles of differing factions of Iraq while leaving aside IS. If at all, the only service President Obama can do is to set 'expectations of those Americans who expect America to solve every police problem of the world'. Luckily for the President most Americans are least concerned with stability of Iraq; what with already isolationist policy expressed by Trump. So long as the fight against IS continues and the danger of domestic terrorism does not increase; Americans are unlikely to support any substantive foreign intervention. Impeding collapse of PM Abadi in Iraq may be bad, but in the end those problems will have to be solved by Iraqi themselves - and that may take decades.
As for the second concern of Iranian influence in Iraq, Moktada al-Sadr whose supporters ransacked Iraqi Parliament, is not disposed well towards to Iran. What it means the immediate danger of increase in Iranian influence is not the case here. Iran is likely to put maximum premium on getting foreign investment and foreign exchange in months to come. Obama Administration can utilize those leverages well to keep Iran engaged and stay away from more mischief in Iraq.
Finally, yes all over the world, folks are going to blame America that it could not get Iraqi government right even after decade long efforts. That blot on America's credibility is unlikely go away soon. Regardless of chatter of neo-cons, both Americans and American political class will need to simply start taking such a criticism in stride. Life has to move on. America's national interests are no longer tied to geopolitical 'oil' considerations. Middle East is unlikely to be stable for years to come. If the global economy indeed moves beyond fossil oil, Saudi Arabia and neighboring regimes might even collapse despite bold attempts to move beyond oil. Iraqi slow train wreck is the preview of that show. But none of these problems can be solved by America's interventions alone. Those will have to be solved by those very people, their neighbors and global action. China, Russia, Europe are more near to unstable Middle East than America and as a result needs to have more stake in those affairs. Donald Trump is already setting that tone. For Hillary, she will have to be careful in avoiding America getting entangled. But all in all, the direction is clear. False pretense to prestige is not going to help America nor further her interests.
In other words, Obama Administration will suck up with what is happening in Baghdad and will simply have to be patient. Same will be the case for new administration next year.
 - WSJ thinks Obama should have kept more American soldiers in Iraq since 2009. It reminds readers that in Vietnam war, both Democratic and Republican Administrations continued this path of slow and steady increase of force application with disastrous results. If WSJ implies that there had been an point in the Vietnam campaign where 'sufficient forces' of USA would have made the difference; that is doubtful. Similarly, having more American soldiers in Iraq would have simply increased American casualties, sapping up any support for American intervention in Iraq. Big part of Iraq's problem is purely political, internal and all to do with it's corrupt political system. Those issues cannot be addressed by American soldiers alone.
 - Donald Trump would not have any credibility in criticizing Hillary Clinton for her aggressive policy in Libya which did not result well. But Clinton essentially 'shoot first and then thought later' in case of Libya; the classic way in which NeoCons of this country react. Libya should work as a perennial lesson to Hillary as and when she occupies Oval Office.