I have never connected from a train to a plane in the US. In India I have done so many times with a 14 hour connection (12301 Rajdhani Express from Kolkata (Howrah-HWH) to New Delhi (NDLS) and then UA 83 from DEL to EWR). Most times I have most of the 14 hours to goof off doing something else. One time the connection became a 4 hour connection due to massive delay to trains caused by dense fog in the Gangetic Plains. That is about the closest I have come to missing a connection. It involved hightailing it from New Delhi station to Indira Gandhi International Airport in a taxi and getting there just as check in was opening three ours ahead of departure. The inbound was just arriving ahead of schedule as I was getting on the check-in queue.
In the US, given the relative ease of bailing on the way and catching a flight if something untoward happens, I'd probably feel quite comfortable with a 12 hour connection from a train to a plane. In Chicago that would practically mean an overnight stay since nothing arrives there from the west before mid afternoon.
Just as a hypothetical example, I would be comfortable with arriving by the Silver Meteor into Washington DC, or Philly or New York (in the morning) and catching an international flight out of IAD, BWI, PHL, EWR or JFK in the evening. But I would not feel comfortable planning to do so through EWR or JFK with say the Crescent which arrives in the mid afternoon, or anything scheduled to arrive later than that. Still IAD or BWI may be feasible with the Crescent for a evening departure.