My own ancestors pre-dated Ellis Island; all arrived between 1849 and 1862 - the Famine Irish. My understanding (clearly you would know better) is that federal laws before the Civil War were largely concerned with naturalization rather than immigration itself. It was the surge of Irish, German, Italian, Polish and other [primarily Catholic] immigrants to the Northeast and Midwest that was the impetus for laws to reign in the numbers.

And let's not forget the anti-Chinese bias in the western states that led to the Chinese Exclusion Act.