Looking at the
House vote on the 1924 act, it actually doesn't seem like party lines were all that important. Southerners and Westerners almost unanimously voted for the bill, and opposition was centered in the Northeast (along with a few votes in the Midwest). My guess is that there was a very strong correlation between the number of immigrants a member of Congress represented and their vote on the bill.
A good way of understanding the Democratic Party in the 1920s is to look at the two major candidates of the 1924 convention:
* William Gibbs McAdoo represented the Southern and Western wing of the party which consisted overwhelmingly of white Protestants.
* Al Smith represented the Northeastern wing of the party, many of whom were Catholic and/or first- and second-generation immigrants (and Smith himself was Catholic)