As Skroe is saying, it only pushed that back a decade or two at most - decades where it seems the US might have more important matters to be dealing with than a Nuclear Iran.
That being said, I find it personally troubling that since the 90s, the US has been extremely hypocritical when it comes to nuclear armament. If the US were committed to actually reducing the presence of Nuclear Weapons (as the entire international community should be), then we should have gotten rid of our own. Why should any country take the US at its word that it wants to get rid of nukes, when the US continues to build and develop their own?
I get that we shouldn't be naive and think that countries will do this. In some sense, we as humans have opened Pandora's box when it comes to nuclear weapons. I just find it hilarious that we're not even worried about China having thousands of nukes like Russia/The US, even though they must have 80 or so (or whatever the number is, Skroe can confirm I'm sure). The point is, just one or a few of these things successfully detonating in a populated area would cause widespread death and destruction on a scale much larger than what happened in Japan.
I know I know, we have ways to "intercept" them. But when you think about it, "Missile Defense" doesn't really exist. We've spent trillions of dollars over the years on something that is unreliable and hasn't t really been tested in real-world situations.
Let's say that conventional ballistic missile defense is even 50% reliable (it's not). That means, for every 2 nuclear warheads that are launched, the chances of just one detonating successfully is quite probable. They've only been tested in very controlled environments and even then, they're not reliable.
Lawrence Krauss has a good bit about why missile defense doesn't exist from a physics standpoint and a real-world standpoint:
https://youtu.be/Q5BlpxyD7rY?t=1236