You're making the rather wild assumption that the train would be going top speed the entire way. Between theexpense of acquiring a sufficiently straight route (280 miles seems to run over Long Island Sound, not around it, and through multiple densely inhabited areas), the ridiculousness of non-stop between DC and someplace as small as New Haven, and the likelihood that they'd have to slow down simply to reduce noise pollution if they didn't go far out of their way to avoid human habitation, there's exactly zero chance of a 90 minute train from DC to New Haven.

Fun to imagine, though.