It depends on the route. It s around 80 hours ( a little more than 3 days) if you take the Southwest Chief or Sunset Limited. However if you want a longer trip the Texas Eagle route take about a day or more longer.http://tickets.amtrak.com/itd/amtrak
Well by driving can be a bit longer... 4-5 days or even 6 days.Train should take at least 3-5 days.
have you looked on amtraks site?