It can happen that you get lucky and snag a low priced room near the departure date, and we always recommend that people keep checking because you just never know. But I sure wouldn't count on it.
For any of you who don't yet do this, I strongly recommend you follow Alan's advice. Continue checking for deals as the departure date gets closer. So long as you only have a reservation and not a ticket you can easily pocket the difference if any lower fares become available. It's already worked out for me multiple times. Just don't ask me to explain
why it works this way because I honestly don't get it.
The reason why it works is because when someone cancels a reservation, the room is returned to inventory at the original bucket price it was sold at, not the currently existing bucket.
For example, let's consider a simplified example. Say that the bucket prices between two cities look like this for roomettes:
Bucket A: $110
Bucket B: $170
Bucket C: $210
Bucket D: $250
(I'm not sure if this is the way Amtrak designates buckets, or how many buckets Amtrak has per route, but this will suffice for this example)
Let's assume that all the roomettes in Bucket A sell out in the first month of sale and by the time you book, you get a room in Bucket C and pay $210.
However, two weeks prior to departure, an individual who booked very early and landed Bucket A needs to cancel. When they do, their room returns to the system at Bucket A.
Now, when you check the prices, you see that a room is for sale for $110 - this was the room that was canceled. Once this room is booked, the next room will be sold at $210 or whatever the current bucket price is.
Hopefully that was clear.
As far as last minute bookings, I've booked an Acela or two about 20 minutes prior to departure (usually just changing an existing reservation for the same day and usually when I'm standing in the station, realizing I can catch an earlier train). It's expensive, but I pretty much only take the Acela when my travel costs are being reimbursed.
I once booked the Vermonter about two hours before departure when I was in college. I and a friend were supposed to get a ride back from another guy and we couldn't get in touch with him on the day of departure. We decided to play it safe and take the train, but it was the Sunday after Thanksgiving, so my Dad had to drive us several stations up the line because the train was sold out until that point. Right before we arrived at the station, our ride called us and apologized - he said that his friends wouldn't give him back his keys until he 'sobered up.' We were both pretty thankful we opted for the train after hearing that.