Most proposals would require some level of English proficiency in order to qualify for naturalization. But as the Migration Policy Institute found in a 2011 report, even seemingly small differences in the level of English proficiency required for naturalization could determine whether millions of people qualify or are left out.
At the end of 2012, Miranda Wilkerson & Joseph Salmons (the latter a member of Team Verb) published "Linguistic Marginalities: Becoming American without Learning English" in the Journal of Transnational American Studies 4.2 (available here). They show that into the 20th century, German monolinguals in Wisconsin weren't marginal in some of the obvious ways people today expect or assume. Lots of evidence shows that the people in these communities considered themselves and were American, and they conclude that "an ability to speak English has never characterized an American identity".
They're building on earlier work where they showed that up to a quarter of some communities were monolingual in 1910, a third of those people born here. And the word on the street is that there's a diss coming that shows considerably higher numbers for at least one community in eastern Wisconsin.
Sure would be nice if people making policy got a little historical perspective on some of these issues.