Why not voting? Current citizens aren't doing it - 60% turnouts for elections and look at the trash voted into Congress. Maybe newly minted citizens will be more informed and care more.
I wish this was true but from what I've seen its wishful thinking. I work with a bunch of (presumed) illegals and they don't make any attempt to even learn english, let alone get involved in our political system. Where I live which is a medium sized city there are probably many thousands of illegals.
They have their own community and have everything they need in spanish available to them, including radio and tv stations. They are just going about their business here in the U.S. but they are not assimilating into our culture, as their community here is large enough that they don't have to.