As Jon said, Republicans (and frankly all politicians) need to be concerned with increasing the number of voters. You do that by having citizens buy in to the political process and also by making it as easy as possible to vote.
If this means early voting on a Sunday, fine. Universal ballot delivery, why not? Same-day registration is a no-brainer. Why not be really bold and have compulsory voting? I know the latter is technically undemocratic but honestly, how many people sit out of the electoral system because of an active, democratic choice to do so?