First Tuesday in January (excluding January 1): Iowa Caucus
Second Tuesday in February: New Hampshire Primary
Second Tuesday in May: Every other state holds a primary
That's a long wait.
And why Tuesday?
I just picked the day when most primaries are held. Plus, I could never deny the media the right to have a "Super Tuesday."
Tuesday elections are an anachronism, from the days when polling stations were a day's ride away and there were proscriptions against travelling on the Sabbath.
I don't see why that matters. Also, every state gives the day off to its employees, similar to the Presidential election day, so that they can vote.