The Constitution actually says
And Congress has directed, in 13 U.S.C. Section 195, which authorizes the Secretary to use the statistical method known as sampling to conduct the census – but prohibits the use of sampling for purposes of apportionment of Representatives in Congress. So sampling can affect the census counts, which are very important to states, as they often determine how much money is given to each state under various Federal programs.
But note that law authorizes the Secretary of Commerce to use sampling; it doesn’t say that he must do so.
That became an issue in 1996, when New York, California, NY city & other big cities sued, claiming that the decision of the Secretary not to use sampling deprived some citizens of their Constitution right to equal representation. The Supreme Court ruled 9-0 in Department of Commerce v. City of New York (No. 94-1614) that the Secretary of Commerce was not required to statistically adjust the 1990 census, despite the Department’s admitted undercount of the overall population and the disproportionate undercount of certain racial and ethnic minority groups. And the Court said that the Secretary’s decision met the requirements of the law, and the Court was not required to intervene.
In 2001, North Carolina & Utah were vying for the last Congressional seat, which went to NC because their census count was 827 people higher. Utah sued over the Secretary of Commerce’s decision to count citizens temporarily overseas (military shipped overseas from NC bases) as legal residents of that state. Utah argued that Mormon missionaries sent overseas from the Temple in Salt Lake City should be counted in Utah. The Court refused to intervene, saying it was within the authority of the Secretary to decide this.
And in a 2002 case, Utah argued against the process of ‘imputation’, where a census worker who finds no one home ‘imputes’ the number of residents of the house, based on how many people he found at similar-sized houses in the same neighborhood. Again, the Court held that the imputation is reasonably consistent with the findings of actual enumeration, and the Secretary of Commerce had the authority to use this process.
So for the last 15 years, the Supreme Court has shown a reluctance to intervene in census decisions made by the Secretary of Commerce. But those decisions can obviously make a big difference in the results. So presumably, the President wants to have a more direct influence on those decisions.