War with Turkey has been on the minds of most Greeks since the Byzantine period, and there have been wars. The last time Greece invaded Turkey in 1922 with the blessings of the great powers, they suddenly found themselves alone when France switched sides and the other powers didn't feel like starting World War II a few years early. The Greek army was defeated and the Greeks who had been living in Asia Minor for centuries were chased out of their homes and back to a country they had never been to. It was known as the Asia Minor Disaster. Since then there have been skirmishes and a war of words that seems to heat up to the boiling point every couple of years.
War is unlikely for the following reasons.
First of all the US would not permit an invasion of Greece. The Greek lobby in Washington is powerful, plus not only does America have business interests in Greece, but Greeks are in control of many major US companies. But the real reason there will not be a war is the situation of Turkey which is surrounded by enemies. An attack against Greece by Turkey would open the door for any, if not all of Turkey's neighbors to come in and perhaps carve off a piece for themselves, not to mention the various ethnic groups within Turkey who can't even be controlled in so-called 'peacetime'. War with Greece would mean the end of Turkey and no country wants to commit suicide.