Federal authority is limited to first, determining when the votes are to be cast so all states do so on the same date; second, confirming the results of the electoral vote, and third, selecting the winner in the case that a majority of electoral votes is not reached by any candidate.
Nowhere is the authority to determine eligibility mentioned. The only thing mentioned is that there ARE minimal requirements to be selected as president. Since the electoral college is who cast votes, then HOW THE HELL are they supposed to make sure they are voting for qualified candidates, unless SOMEONE makes sure of the qualifications?
But that authority is NOT given the federal government, anywhere.
So we get to this:
The powers not delegated to the United States by the Constitution, nor prohibited by it to the States, are reserved to the States respectively, or to the people. [\quote]
The power to determine eligibility is NOT delegated to the federal government, NOR is it prohibited to the states. Therefore, it is "reserved to the States respectively, or to the people." Obviously (at least to people with brains instead of donkey shit in their skulls) the people are not going to, individually, determine eligibility. In fact the courts so far have ruled that the people, individually, do not even have the authority to question eligibility. Therefore, the only one left standing to exercise the authority to determine eligibility ARE the States.
Not really. The President of the Senate could easily exercise that authority.