Doesn't the Constitution pretty much leave the issue of registration up to the states, so long as there is not an equal protection issue? This is more an issue of convenience. The poor are less likely to have computers and the identifications like drivers licenses that would be necessary for online registration.
Good point, but the Feds can always get it done by handing out money to the states, assuming it is not unduly coercive. As a Constitutional matter, aside from that, there might be a distinction between elections for state office and federal office. I don't know.
Well, the federal government has ultimate authority to legislate for federal elections per the often overlooked bolded part of Section 4.1 of Article I: "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 Places of chusing [sic] Senators."
As far as that applies to voter registration for federal elections, I'm not entirely sure.
Surprisingly enough, Georgia established online voter registration last year.