Warning 1: Attorney does not ask you if you are a citizen of the United States
Even if you look and sound "American" and have an European sounding name, a criminal attorney who has successfully represented immigrants will be keenly aware that being deported or losing status is probably the number 1 concern of an immigrant. If he does not ask, it should be one warning sign that the lawyer is not showing the appropriate concern for your top issue and you may be in the wrong office.
Warning 2: He cannot give you a name of a single Immigration Attorney he has befriended
If not, it is because s/he is also an immigration attorney. Or s/he does not feel the need to talk to an immigration attorney about making sure you don't lose your status or get deported, and has not bothered for any previous client either. I would run.
Warning 3: Criminal Attorney brushes off your question about immigration with a boilerplate statemente
When you explain (if the attorney has not already asked) that you are not a US citizen, the attorney simply states that s/he can't make any promises about whether any conviction will get you deported or not. This means attorney does not care, and is probably not the attorney for you.
Additional resources provided by the author
Contact an Immigration Attorney who is familiar with immigration consequences of criminal convictions and make sure your criminal attorney is willing to work with your immigration attorney.