Yes, if you go down to the station you can pay in cash. You should go quickly, as the price can go up as more seats get sold. Or if you cannot get there right away, you can call and make a reservation by phone without actually paying. Depending on just how close your travel date is, Amtrak will hold the unpaid reservation for a period between 24 hours to as long as 7 days. The agent will tell you at the time of booking the date by which you must pay or the reservation will automatically cancel and you will lose the price.
