Setup: Earth, current day. US president decides to attack fictional country of Lalalistan, because terrorism/drugs/whatever. This attack has big support in NATO countries and Russia with China officialy object the attack, but remain neutral. (Example: Lybia attack).
So, while it is officially NATO action, it is mainly driven by US Army.
The twist The dictator of Lalalistan sealed a deal with the devil and obtained Death Note and Name vision
=== For those who do not know how Death note works: ===
If you know Anime series Death Note, you can skip this section, because the dictator of Lalalistan obtained exact Death Note as used in this Anime series. So for these who do not know how the Death Note works:
- Death Note is magical artifact in form of usual paper notebook
- The human whose name is written in this note shall die.
- This note will not take effect unless the writer has the person's face in their mind when writing his/her name. Therefore, people sharing the same name will not be affected.
- If the cause of death is written within the next 40 seconds of writing the person's name, it will happen.
- If the cause of death is implausible, or not specified, the person will simply die of a heart attack.
- After writing the cause of death, details of the death should be written in the next 6 minutes and 40 seconds. Source
The Name Vision works simply: If you look at a person (even through video recording), you can see their real name and therefore write it into the Death Note correctly.
=== End of Death Note mechanics explanation ===
Lets give the country of Lalalistan shape: The Libya example could work well: Lalalistan is about as big as Libya and has military force of Libya a year before NATO attack. However, it differs from Libya in two details:
First, the people of Lalalistan support their dictator and think that the NATO attack is act of aggression and second, I doubt that the fine people of Libya ever dealt with a devil.
The question: Could the US military with joint help of other NATO countries sucessfully attack this country without using nuclear weapons?
Also, bear in mind, that the Death Note is only one example in this world and the artifact works even if you tear the pages to small pieces.
To add more details: If only names should be written into the notebook, and someone clever would be using the notebook, you could fit in 250,000 names. The dictator is not that clever, so lets give him capacity of 100,000 names before the Death Note is fully used.