Since World War II, the wars that America remembers with least fondness are its counterinsurgency struggles: Vietnam, Iraq, and Afghanistan. They were seen as long, drawn out, and unsuccessful. They were considered failures because after the US got tired of the protracted struggle and left, the enemy just moved into the vacuum left behind. The wars the US remembers with fondness (or doesn’t remember at all) are El Salvador, the Invasion of Grenada, the Invasion of Panama, the Gulf War, the air campaign over Bosnia, the early stages of Afghanistan, and the Iraq Invasion. This is largely because these wars were successful. With the exception of El Salvador, they were short, sharp conventional wars that resulted in overwhelming victory.
These examples demonstrate that the US fares much better in conventional wars than it does in counterinsurgency operations. The obvious lesson for American strategists in this history is that if US has enemies that it needs to defeat, it should avoid counter-insurgency campaigns (except when they can be done on a sufficiently low level so that they can be maintained comfortably over an extended period of time - like El Salvador), while maneuvering to defeat its enemies conventionally.
The problem with going into Syria to defeat ISIS is not that the US cannot crush the Islamic State militarily. On the contrary, one heavy armoured division, sufficiently supplied, could romp across ISIS-held territory in a matter of weeks. The problem is that ISIS won’t put up a fight because they know they will lose.
There is a story floating around that ISIS actually does what an apocalyptic confrontation, where they can defeat evil finally and for all time. Their ideology is said to favour the village of Dabiq, just north of Aleppo, for this apocalyptic battle. If I though that ISIS were actually serious about this, then I would be the most enthusiastic supporter of a ground invasion around. ISIS is a rag-tag force of incompetents and lunatics. In a pitched battle, they will lose - and fast. Killing them to the last man would be a great way to get rid of them for good. But I doubt they will be that much of a cooperative adversary.
The one type of war the Arabs have shown themselves to be good at is guerilla war. In all likelihood, instead of seeking the apocalypse, they will melt away among the masses, leaving the US Army with a Pyrrhic victory. A few months after that victory, the guerilla war will begin, with a car bombing here, a sniper there, and a suicide bomber yesterday afternoon. This will force the US into a long, grinding counterinsurgency operation that will take a decade to win, and will require over 100,000 men on the ground for that entire time. And in the end, all we will end up controlling is a strategically worthless piece of real estate (while magnanimously allowing the Chinese to buy the mineral rights, as was done in Afghanistan).
We have seen this movie before. Do we really want to see it again?