The setting:

• Present day. The country is up to you. Whatever would be easiest.

The guy:

• Highly skilled. Maybe ex-Marine? Special forces? You can have him be "top of his class" at just about anything, but not a genius or a superhuman.
• Has a death wish, but like, for everyone. He knows that he won't come out of this alive, and he doesn't care. He just wants the whole world to burn. Total human extinction if possible.

The duplicator:

• Shaped like a gateway large enough for a car.
• Only works once. Once you hit the button, it stays on, producing the exact same thing over and over, with no option to change what it makes.
• To activate, fill up a car with whatever supplies you want duplicated (i.e. a car containing you, your savings in cash, provisions, C4, guns, and ammunition), then hit the button. From that point on, an endless line of cars driven by clones of you drives out of the gateway at a rate of about 5 per minute.
• All duplicates are created at once, so the duplicate who drives out 4 hours after you hit the button has been driving for 4 hours (they come out of parallel universes; I don't want to get into it). They can refuel and replenish their food supplies in the other universes, so don't worry about that, but their need to sleep might impose time constraints.
• Can be placed anywhere (the limiting factor is where to park all the identical cars). Can't be moved after the button's been pressed.

The question:

• Can this guy and his duplicated army get past a country's defenses and launch their entire nuclear arsenal?

The way I see it, he has a well-coordinated, well-equipped, and talented army that can assemble innocuously in a matter of hours or days, so it seems plausible that he could overpower them before reinforcements arrive. Then again, he doesn't have nuclear codes or any clear way to get them. Does he stand a chance? Are nukes even his best option?