If Iran walked into Iraq, they would also have too much to handle. Iraqi's and Persians have hated each other for centuries. They fought an incredibly bloody war not that long ago. Iran would be in the same situation we are now, fighting an insurgency with no end in sight.
The Shia majority of both countries belie that argument. If we pull out with the government as weak as it is, Sadr will rise to prominence and he spends more time in Iran than he does in Iraq. Iran will have NO problem subduing Iraq since it will have absolutely no qualms when it comes to civilian casualties that we have.