across the nation vs across the country

across the nation and across the country both are adverbs.

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

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

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

Other synonyms of across the nation include nationally, nationwide.

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