Dear Users,

Is this idiom a commonly used one in the English-speaking countries? Can it be used in the following way?

I'm a mile behind with grading but I should be done by tomorrow.

Does it simply mean: I'm overhelmed by work; I'm up to my eyeballs with work?

It's pretty much not used at all, and no it can't be used to mean what you want. Mostly because a mile isn't very long. You could say "I'm miles behind" to get your meaning.
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You absolutely can use it in this context and, contrary to the other reply it is a widely used phrase in English speaking countries, particularly in Hiberno and Anglo English

Further a mile is long enough, about 1.3kg so when used in the context you have stated it adds to the magnitude of how far ‘behind’ at something one is.

Also, it would be more commonly used thus; ‘I’m miles behind at/in...’

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