Certainly unions don't support Republicans and vice versa.
Here's a site that shows contributions by industry:
http://www.opensecrets.org/overview/industries.asp?cycle=2006
Here's another look at the data by organization from the same site:
http://www.opensecrets.org/overview/topcontribs.asp?cycle=2006
Fact is there isn't a union out there that is even on the fence much less a Republican supportor. All lean to or are strongly Democratic.
As to immigration I think the conventional view (that Republicans don't support legal immigration) is wrong too. An opinion piece that sums it up pretty well in my view. Both parties are playing both sides on this issue- with the typical political hypocrisy.
http://www.speakout.com/activism/opinions/5672-1.html