Four days from Boston to NYC, 6 weeks from Chicago to NYC. In a stagecoach, I presume, with no shock absorbers.

All you would need is some track through Alaska/Yukon, a tunnel under the Bering Strait, and more track in Siberia – and voila, you could connect three continents by train. That would be one long ass haul from New York to Paris by train via Siberia but it might be possible one day.