nationally vs across the country

nationally and across the country both are adverbs.

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

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

nationally and across the country: extending throughout an entire nation

Other synonyms of nationally include across the nation, nationwide.

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