Marketing won't help one bit. Complete waste of time.
On the contrary, an effective marketing campaign would work wonders for Amtrak. You underestimate the number of persons across the nation who are largely or completely oblivious of the company's existence. Even if they are vaguely aware passenger trains are a travel option, they don't have a clue where or when they operate, how or where to buy a ticket, or even where to get more information (hard to believe in this day and age, but true). The "option" isn't even considered; It's not part of their world. Even in cities with decent service and (typically) reasonably reliable trains, such as Savannah and the Carolinas, too many people aren't aware of the train.
Yes, there are problems - serious problems - ranging from late trains, to onboard food service, to a myriad of other service issues. But to wait until such problems are completely solved is really just another way of saying "never". While timekeeping needs to improve greatly from current levels, there will always be late trains (just as there are late or cancelled flights or buses, and you don't see the airlines canceling marketing efforts until that changes). Improve food service with diners on all long-distance (and perhaps some regional) trains and revamp cafe lounge offerings, but never doubt once you do there will remain further problems (food is too expensive, limited selection, etc.).
All such service issues need to be addressed (thoroughly and immediately), not so much to attract new passengers as to retain the ones you already have, but that doesn't mean you can ignore ridership (marketing) while you work on things. Can you imagine how it would play in Congress to see significant and continuing ridership declines while we wait on better service in the future? Indeed, for all the shortcomings and ineffectual marketing the long-distance trains notably
aren't seeing declining passenger numbers; Attracting new business also makes the trains look much better to legislators who are often hostile to providing an operating subsidy, and a potentially more generous budget makes solving all those service issues far simpler (or even possible).
However, to realize untapped ridership potential we absolutely must address the issue of capacity. Many or most trains - LD in particular - just don't have the available seats for large numbers of new passengers (note also the rationale for new high speed train sets). If you want to see significant increases, the trains are going to need more than the "standard" four coaches and two sleepers (with some variation, of course). So while we work on service issues and the like, we're also going to need a major order for new cars (150 more Viewliner coaches and lounges would simply replace the Amfleet II cars at current levels, leaving no room for increases). Ridership numbers far below 100% often represent sold-out trains (full over a portion of the route but plenty of empty seats at the ends); The objective should be increases in total numbers of passengers carried, though filling empty seats towards the end points of a route does appear to suggest a potential marketing approach.