I was looking for specific statistics on this. I couldn't find any quickly. Of course "legal immigrants" is a pretty broad group that includes H1-B visa holders from Western Europe and India to Syrian refugees. I am sure that there is a very wide range of opinions.
I do volunteer work in the immigrant rights movement. I know a lot about this group (which doesn't say too much about the society at large).
There is a lot of crossover support from legal immigrants. There are many groups that support immigrants without any regard to status, the prime Minister of Ireland recently spoke out about the rights of undocumented workers (including about 10,000 Irish people) in Boston. On the other hand I do have a co-worker, a legal immigrant (tech worker) from Turkey, who rails against "amnesty".
And the immigration issue gets very messy... many legal immigrants (particularly from Latin American or African countries) have family and friends who are undocumented. People go to church, and make friends, and are neighbors, brothers and spouses with undocumented immigrants.
Once you know people in this community... once you know real human beings who are facing these issues... it seems from my experience you are far more likely to support rights for undocumented immigrants.