Do people make these kinds of distinctions, or are they simply more or less favorable to immigrants? I found a CBS News/NY Times survey from 2011 which asked "Should legal immigration into the United States be kept at its present level, increased, or decreased?" and "Which comes closest to your view about illegal immigrants who are currently working in the U.S.? 1. They should be allowed to stay in their jobs and to eventually apply for U.S. citizenship, or 2. They should be allowed to stay in their jobs only as guest workers, but not to apply for U.S. citizenship, or 3. They should be required to leave their jobs and leave the U.S."
There is an association between opinions on the two issues--for example, 50% of those who say that immigration levels should be increased and only 26% of those who say that they should be reduced choose "should be allowed to stay in their jobs and apply for citizenship." But the association is weaker than the association between opinions about same-sex marriage (allowed/civil unions/no recognition) and abortion (allowed/with restrictions/not allowed), which are certainly two different issues. In fact, the correlation between views on same-sex marriage and treatment of illegal immigrants is as strong (.22) as the correlation between treatment of illegal immigrants and desired immigration levels (.21). So people do seem to treat the two issues as distinct, although related.
More educated people, people in the Northeast and West, Jews, and people in urban areas take more liberal positions ("increased" and "allowed to stay") on both issues, and evangelical Christians take more conservative positions. The samples of blacks and Hispanics were unusually small for this survey, so it's not possible to say anything definite about ethnic difference. The effects of age and gender, however, can't be described as simply liberal or conservative. Young people are considerably more likely to favor increased levels of immigration, but no different in views of policy towards illegal immigrants. Women are more likely to say that people who are here should be allowed to stay and apply for citizenship, but also more likely to say that immigration levels should be decreased.
[Data from the Roper Center for Public Opinion Research]