Yes, this can be done in Marketo.
1. Do you have the Data Due Date field already in Salesforce on the Opp or Lead? If not, please expose it on the page layout.
2. Your campaign will look like
Smart List: Trigger: Opportunity is Updated: Attribute is Status with New Value IS "X" with constraint Data Due Date ON OR AFTER "X"
or something like that. Not sure what Data Due Date is really saying there, so you might need to play with the operator on that.
You can also do a non triggered campaign as you mentioned, just use Has Opportunity instead.