Do you have an American residence? If you have it it is not a problem. If you do not have a US residence and only have a visa, you can visit only for the period of time you have until your passport expires. So, if you can cross.
I don't think they let him board.
I passed with my expired passport but I don't know if it was a stroke of luck ....
I am Mexican I have the residence but only the passport expires next month
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