“Section 1. All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States...
“Section 2. Representatives shall be apportioned among the several States according to their respective numbers, counting the whole number of persons in each State, excluding Indians not taxed.”
In theory, Amendment XIV might require perfect accuracy, which is impractical.
“apportion electoral votes as the census does?”
Amendment XIV seems to require an actual counting for apportionment.
The federal government probably could figure out from government records and cell phone company data, to about .01% accuracy, how many citizens are in any given state at 3am in the morning.
Include the rest of section 2:
Representatives shall be apportioned among the several States according to their respective numbers, counting the whole number of persons in each State, excluding Indians not taxed. But when the right to vote at any election for the choice of electors for President and Vice President of the United States, Representatives in Congress, the Executive and Judicial officers of a State, or the members of the Legislature thereof, is denied to any of the male inhabitants of such State, being twenty-one years of age, and citizens of the United States, or in any way abridged, except for participation in rebellion, or other crime, the basis of representation therein shall be reduced in the proportion which the number of such male citizens shall bear to the whole number of male citizens twenty-one years of age in such State.”
So, everyone gets counted, but apportionment is reduced by the number of inhabitants who are not eligible to vote.