They say the Constitution of the United States doesn't mention sampling. Of course, it also doesn't mention airplanes or telephones. That hasn't stopped Congress from using modern statistical techniques to regulate them. What's really driving the Republican objections is politics. Areas that are undercounted are primarily low-income.
People there tend to vote for the other party.
Texas, which unfortunately contains a disproportionate number of poor folks, is one of those states particularly hurt by the undercounting. The battle over sampling has been going on for some time in Congress. A compromise plan squeaked through Congress last November. It calls for a dress rehearsal. Sacramento will be counted using sampling.