What does history teach about the need for a nation to have a common/national/official language?
As always with history's lessons, the message is mixed. One could argue, I suppose, that the worst war in U.S. history was not caused by language--that the South and North didn't speak different languages. And if we look north to Canada while we've seen signs over the years of strains caused by two official languages, they've survived pretty well with much less bloodshed than we. And if we look south to Mexico and beyond, we're reminded that multiple (native) languages can cause problems, but don't necessarily mean division.
Personally I'd look to economics. Whenever two people with no language in common get together, they try to trade, either goods or sex. (Simply follow GI's in foreign countries.) To oversimplify, as long as our immigrant population is part of the U.S. economy, they'll become "Americans", regardless of whether they become citizens or not.