Not that the Constitution matters to these people any more, but does not the same spell out that each state has the authority to conduct elections? Can the Senate vitiate state authority that easily?
Article I Section 4 gives state legislatures the power to set "The Times, Places and Manner of holding Elections for Senators and Representatives," however it gives Congress the power to alter those state powers.
Article I Section 4:
The Times, Places and Manner of holding Elections for Senators and Representatives, shall be prescribed in each State by the Legislature thereof; but the Congress may at any time by Law make or alter such Regulations, except as to the Place of Chusing Senators.However, Article II Section 1 gives the state legislatures the power to conduct elections for Electors to the Electoral College, and Congress has no power to alter these elections except for the date on which it occurs.
Article II Section 1:
Each State shall appoint, in such Manner as the Legislature thereof may direct, a Number of Electors, equal to the whole Number of Senators and Representatives to which the State may be entitled in the Congress: but no Senator or Representative, or Person holding an Office of Trust or Profit under the United States, shall be appointed an Elector.This means that if Congress chooses to nationalize Congressional elections, the states will have the option to split the ballots into Presidential elections, Congressional elections, and local elections. Each ballot would have its own set of rules, with only the Congressional elections mandated by the Election bill.The Congress may determine the Time of chusing the Electors, and the Day on which they shall give their Votes; which Day shall be the same throughout the United States.
However, in practical terms, the states would likely conduct all elections the same way for cost and convenience reasons.
-PJ