Save face from whom?
Americans or foreigners?
The "face" of the government has already been tarnished. And they are making this country look horrible as the days go by.
Not only that, but people actually think that we are losing this war if we pull out.

I need to ask. When do we WIN? What constitutes victory for US? This isn't even our war anymore. It's a huge foreign policing effort. People are sick of it, inside and out.
Regarding Iraq you are pretty much correct. When I left in the middle of June we were almost finished with the Battle of Mosul- the last stronghold of the foreign fighters- AQI. Once that is over, the US could very well declare victory. The internal squabbles of Iraq will continue until the end of days.
Of course the US still has a national security interest to keep some bases in Iraq to watch over the oil fields of the Middle East. That is until we eliminate oil as the main liquid fuel. Then we could leave and let the region descend back to the 7th century AD.