across the country vs nationally

across the country and nationally both are adverbs.

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

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

across the country and nationally: extending throughout an entire nation

Other synonyms of across the country include across the nation, nationwide.

across the country (adverb)	nationally (adverb)
extending throughout an entire nation	extending throughout an entire nation
	with regard to a nation taken as a whole