Of course. But right now the ideology doesn't have to present any other bulletin point than "Look how the West is mistreating us."
This is less about what the US actually did and what the actual consequences of that were. To be honest, I think the consequences of US involvement are far less than what the Extremists claim them to be. But that doesn't matter. What matters is who's on the ground in those regions (ISIS), who's in control of the information on that ground (ISIS) and who's believed (ISIS).
So anytime a bomb falls, some of those people think "Gosh, they're right..."
As false as that may be, that's most likely what's going on there. Thus involving the US any more than they are is like holding a red cloth in front of a raging bull.
And the other aspect is, no offense, that the US tends to behave rather rudely in those countries. Local customs and practices are largely ignored, power balances are misinterpreted and consequences are not thought through. Removing Saddam in itself is a goal everyone on the planet can get behind. But doing so without setting up a followup to Saddam was reckless at best.
Would it change anything if the US admitted that now? Nope. Not one bit. The best we can do with that knowledge is to contain the crisis, not do any similar rash action that cannot be reversed and think about what it is they actually want.
Robin Hobb once wrote for one of her characters a line that's so smart it needs quoting here "Don't do what can't be undone before you've considered what you can't do once you've done it." It's time to start thinking really hard about ISIS and counter-propaganda on Fox News is not it, I'm sure we can all agree on that. Europe may be the key. Not despite the high muslim portion in the population but because of it.
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I doubt that. Everyone knows our military is a joke. Nobody wants us to flex our industrial muscles again. Not that way.