It is the mixing of terms that has us at odds.
Refugees are not immigrants.
Illegal immigrants are not immigrants.
There is no law that says anyone traveling to this country, legally or otherwise, is entitled to citizen status.
Last time I checked, we were still a sovereign nation. Citizenship is not something that can be easily revoked. It should likewise not be something easily obtained.
Thus, it is, or should be, extremely difficult to abrogate the legal requirements of being a citizen of this country. If we do intend to go down that path, we should be very aware of the unintended consequences before committing.