The Census resisted privatization of data collection for many years. When it was finally imposed "the privatization led to rapidly escalating costs, reduced productivity, near catastrophic failures of the 2000 and 2010 censuses, and high risks for the 2020 census."
If you are looking to contract to save costs, maybe the defense industry is not the right model. 
Other countries do censuses, and have incorporated information technology without relying on private contractors that have driven up costs. Two US military contractors struggled with this task to the point that the 2010 Census ended up being paper-only. Both got paid $1B each.
It is fair to note that there has been a good deal of research within public administration on how contracting for complex or unique services result in contractor capture and failure, e.g. Brown, Potoski and Van Slyke watermark.silverchair.com/mup034.pdf?tok…
