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Canadian (or US) border agents do not usually check your driver's licence (unless you are travelling on an EDL as an American/Canadian citizen).
However, driving on an expired licence may be illegal in the U.S. for you. Police checks can happen independently to immigration and customs checks, and your insurance coverage may be invalidated.
In Canada, if you ...
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You have two separate concerns:
Immigration. Canada will want to see a valid passport and Canadian visa. They don't care about your driving license. Likewise the US wants to see you're eligible for re-entry on the way back, which in turn depends on your current I-94 status and other documents, but not the driving license. If you want an answer related to ...
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