Iran could absolutely beat the US in a war. It wouldn't be good for Iran, but it sure as shit would get interesting around the time we get to watch a US aircraft carrier burning and sinking into the Strait of Hormuz on CNN.
I recognize that Iran isn't like Iraq, but would Iran realistically have a chance of beating the US? I would expect us to be able to park ships outside of their range and destroy military targets with relative impunity. Maybe I'm underestimating how sophisticated Iranian missiles are, since long range missiles are the only way I could see them even striking an aircraft carrier. Iran has a lot of military tech from Russia, right? Maybe it is better than I realize.
I'm kind of curious now how effective ship based point defenses are against modern missiles.
No, Iran does not. Not in the conventional military sense. Certainly invading Iran is going to likely lead to the same insurgency/I-don't-want-soldiers-parked-on-my-street-setting-up-checkpoints type of rebellion problems that we had in Iraq, but in the conventional sense Iran isn't remotely a threat. We have antimissile defenses and have been working on them for years because missiles are the best way to destroy a carrier group and our military isn't made of idiots, we have missiles of our own with better range and guidance and warheads, we've got better aircraft capable of getting in and destroying their military defensive infrastructure (including the radar sets that would allow them to find targets to launch those missiles at and the missile launch sites they need to actually, y'know, launch the missiles) without even getting spotted, etc.
In short: No, Iran has no chance. It would be a campaign likely on par with the initial coalition invasion of Iraq in terms of swiftness and casualty rates. There's just no way for a third-world country relying on old Soviet-era exports and a few modern weapons (if Russia has been providing them modern equipment, I don't know one way or the other) to feasibly pose a threat to a competently run first-world military in a meaningful way.
As for the resultant insurgency, massive changes in the way the following occupation and rebuilding efforts would be required to avoid and/or mitigate that, otherwise we end up right back where we started---losing a small number of troops overall but in ways that make it impossible to find a simple and easy solution, making continued involvement politically untenable.