Immigration does not fit into the Democratic-Left/Republican-Right split. Both parties have pro-Immigration and anti-Immigration parts that don't get along.

For the Democrats it is no human is illegal liberals vs union democrats. For the Republicans it is the good for economy economists vs the Law and Order types. In each case there is also a radical fringe that the party would rather pretend doesn't exist.

The Republicans seem to be having a harder time with it though because pits the law and order rank and file against the pro-business leadership. On the Democratic side the split goes the whole way up the party and isn't quite as big.

Jay