Throughout our history many states have allowed legal immigrants to vote. Some states have set the bar as low as making the immigrant say "I'll become a citizen when I'm allowed" in order to cast a ballot. This is merely a political tool utilized time and time again. The power party will limit or extend a states voting dependant on what they see as the majority immigrant political inclination. In the midwest legal immigrant voting was widespread until the "slavic scare" of the early 1900's whereafter it came and went according to the above. It's no surprise to see places like New York or San Fransisco take very open views when it comes to noncitizen voting at this time.
The U.S. Supreme Court has consistently ruled to uphold the states' right to set voting registration and qualifications while at the same time stating that immigrant/noncitizen voting does not violate the Constitution. The only apprehension the Supreme Court has had in these matters is voter fraud as seen in their upholding of the Voter ID laws to challenge this last year. With 3000 dead people voting in New York last year, I'd say we have a problem with voter fraud.
The problem is as always, the current state of immigration and our poor border control. Despite the rhetoric, this problem will not go away within our lifetimes. Why? As stated above immigrants, their votes, and their activism is a political card to be played when its convenient, nothing more. Actually fixing the problem now and working ahead for something better would cost too many people their jobs on the hill.
Bookmarks