Our office has prevailed in arguing food stamp trafficking (in the State of Ohio) is not a deportable offense. The RSP charge has also been routinely defeated. There are other considerations and your should hire a deportation attorney prior to proceeding with your criminal case.
There are a number of variables, but if this is YOU or a family member, friend, etc. make sure to consult with an immigration attorney who is knowledgeable about immigration consequences of criminal conviction, to provide advice also to criminal defense lawyer. It is important to obtain advice prior to any resolution of the criminal case. Again, make sure to consult an attorney who is knowledgeable about the immigration consequences of a criminal conviciton.
I agree with my colleague that consulting with an experienced immigration lawyer and an experienced criminal defense lawyer is essential. From the immigration lawyer, you need to know what type of charge the offense (such as whether it is viewed as a Crime Involving Moral Turpitude? etc) is considered by the feds for deportation issues; and, from the criminal defense lawyer you need to know what the possible resolution of the charge is. You can then make an intelligent decision on how to resolve this charge, understanding both the collateral impact on deportation and the direct impact of the possible sentence (jail/fine, etc). Good luck.
DISCLAIMER I do not practice law in your State. This answer is provided solely for informational purposes only. This answer does not constitute legal advice, create an attorney-client relationship, or constitute attorney advertising.