It depends on what the "white collar" offense is, but generally no, with exceptions. For example, false statements, mail fraud, wire fraud, health care fraud and bank fraud have no mandatory minimum sentences by statute. However, aggravated identify theft has a two (2) year mandatory minimum sentence, and must be imposed consecutively to any other sentence imposed. If you can be more specific about the type offense without publicly discussing the specific details of your particular case, I can provide a more specific answer.
Others have already correctly answered; there is no minimum sentence on "white collar" crimes with the exception of Aggravated Identity Theft which is 2 years consecutive to another offense.
In the Federal system, sentences are based on many things, but the dollar value of the offense is one of the major considerations in calculating a sentencing range.
If you have not yet been indicted but think you may be, you should consult with an experienced attorney. Consultation before you have been charged, when the attorney could perhaps speak with those who are investigating you might be especially helpful.