Amtrak's official baggage policy says they enforce it "strictly." The size limit of a carry-on bag "may not exceed 28x22x14 inches in size." There is only a limited amount of space on the luggage rack so this is understandable.
See: http://www.amtrak.com/servlet/ContentServer?pagename=Amtrak/am2Copy/Title_Image_Copy_Page&c=am2Copy&cid=1080080553878&ssid=43
Note that certain items including "briefcases, purses, laptops, and infant paraphernalia such as strollers, diaper bags and car seats" are not counted against your carry-on limit of two suitcases.
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