my plant kept thirty days supply onsite.
Gov't emergency managers are well aware of eletric grid's status and needs. Fuel delivery will get high priority.
In theory a nuke plant could "island" and provide its own house power but we never did. There was one morning when all outgoing power lines went down because of unusual weather and were left as a local island with an adjacent fossil plant. Our house load amounted to around 20% of Mr Fossil's capacity so like '3 men in a tub' we just waited for system to reconnect us to grid.
Nuke plant didn't experience a loss of offsite power because of the fossil unit next door and shared switchyard.
There's a lot to be said for diversity.