Judeo-Arabic as a national language? I am aware that prior to the Zionist movement, the various Jewish "ethnic" groups had their own language, using some dialect of Hebrew, biblical or rabbinic, as a scriptural and liturgical language. The Ashkenazim spoke Yiddish, a Teutonic (West Germanic) language with Slavic and Turkic loanwords and features (and often written right-to-left in the Hebrew abjad); the Sephardim spoke Ladino, a descendent of Latin related to Spanish and Portuguese; the Mizrahim spoke Judeo-Arabic; Ethiopic Jews spoke some dialect related to Ethiopian.
I can not imagine how Judeo-Arabic would become a national language. There are several problems. First, the Zionist project was almost entirely an Ashkenazic endeavor, the Ashkenazim spoke Yiddish, not Judeo-Arabic. (For any Jewish dialect or idiom to become a national language would require the establishment of a Jewish nation-state, i.e. Zionism. Given that many, if not most, Judeo-Arabic speakers lived in or around the Holy Land, there would be no need for them to start a Zionist program as most would already live there, and attempting to found a "Jewish state" would only provoke problems.) Furthermore, as many Ashkenazi Jews abandoned Yiddish for proper German or Hungarian, or Russian, Czech, Lithuanian, w/e Balto-Slavic language, Mizrahi Jews and those Sephardi Jews living in North Africa or the Levant to abandon Judeo-Arabic for "proper" Arabic with assimilation.
Second, given the Zionist movement's concern with establishing a "Jewish race" or "Jewish ethnicity" for the purpose of establishing a nationality, and a continuity with the biblical Hebrews, Hebrew would have to be the national language. Zionists would select a language common to all peoples of Jewish faith (even if only for religious purposes), and which would have been spoken by the original Jews.