If emigration from the British Isles after 1800 did not go to America with possibly increased immigration from Central Europe and Russia how might the use of language develop in the growing USA???
But the point is that the original 13 colonies that formed the first US were all solidly English speaking. So all immigrants arriving past 1800 would land in a country that already had a predominant language and although they would retain their own tongue in their own circles, they would learn and use English for all dealings with outsiders and official state instances.
Adding to this, many of the European countries themselves barely used their official language for anything else then official documents and trans-regional publications. Many regions using their own dialect with often significant differences from the state language. So an immigrant from Sicily would speak Sicilian and feel no different to using English then to using mainland Italian. In fact many of the settlers, in particular the Germans emigrated because post 1815 their states started to exert too much influence on their native region, the replacement of the regional tongue with government language (in Germany Hochdeutsch-High German) often being the most prominent sign of this.
To say it bluntly: Once the declaration of independence was written in English, this was to be the language of the new nation. To change this, you would need a POD before 1776.
That being said, I can easily imagine a USA where the great English-only drives of 1917 and 1942 did not happen and several regions retained their own languages, be it German, Spanish or Cherokee, for daily use. Just as well, I could see a push towards an American English language that openly encourages backfeed from the native dialects instead of purging every idiom that isn't sanctioned in the King James Bible. I mean, US English already has the word 'okay', which depending on the source is either French or native American. There are several instances where words of the local language would fit much better then English, so may be in a different universe, US English would regularly use
'tambien' instead of 'me too'
or 'jawohl' for a more expressive form of 'yes'.