The phrase "national stature" refers to how recognized and respected an individual or organization is on a national level. It indicates their influence, prominence, and importance within a country. Full definition
Suddenly, with the stunning win on gay marriage, Cuomo has become a political figure of national stature, even a possible presidential candidate. (downtownexpress.com)
The collection achieved national stature with the acquisition of the John D. Rockefeller III Collection; his 1979 bequest combined with his wife Blanchette's bequest in 1993 totals 110 paintings, and comprises the Fine Arts Museums» single most important gift of art. (deyoung.famsf.org)
Rose Bowl Day 1933 brings triumph and added national stature to Southern California Trojans, as they crush the highly regarded Pitt Panthers 35 - 0 at Pasadena. (si.com)