On Amtrak, there are no specific days that are cheaper - unlike airlines, where travel on Tuesday and Wednesday can generally be cheaper. It all depends on how many tickets are sold on that train at that time. Amtrak sells tickets using a bucket system. (A ticket on today's train in 2 hours may be less than a train in 3 months! On routes with more than 1 train a day, the 1 PM train's fare may be different than the 3 PM train's fare!)

The only sure thing is the earlier you book, generally the lower the fare. You never know when the next ticket is in the next bucket. Most times, the fare later can only be higher.