across the country vs across the nation

across the country and across the nation both are adverbs.

Word	Noun	Adjective	Verb	Adverb
across the country	No	No	No	Yes
across the nation	No	No	No	Yes

As adverbs, across the country and across the nation are synonyms defined as:

across the country and across the nation: extending throughout an entire nation

Other synonyms of across the country include nationally, nationwide.

across the country (adverb)	across the nation (adverb)
extending throughout an entire nation	extending throughout an entire nation