The charge is made in a letter House Republicans - including Minority Leader John Boehner - sent yesterday President Obama - calling on him to "reconsider and reverse this harmful course of action."
In response to questions from CBS News, spokesman Ben LaBolt says the charge is not accurate.
He says the Census Bureau and the agency's director will continue to work at the Commerce Department.
However, the spokesman says that "White House senior management will work closely with the Census Director, given the number of decisions that will need to reach the president's desk."
The White House also says the same congressional committees that had oversight of the Census Bureau during the previous administration will retain that authority.
Boehner and other House Republicans also used a news conference today to express concerns that the White House will "undermine the goal of having a fair and accurate census."
Mark Knoller is a CBS News White House correspondent.