In the summer of 2000 I did cross country trip in my old 1983 VW Dasher 1.7 l Diesel. It had 200K when I left and 6 weeks later I had 220K on it. My trip took me from Seattle down south to LA than across south to Florida up north to NYC and back west to Seattle. Of course plenty of side excursions, national parks, etc. Car had 3 occupants, got an oilchange halfway trough and averaged 55 mpg. It did not go faster then 60 mph but was able to cross mountains etc.
I think you will be fine in your car. Just to be on the safe side sign up with AAA or the Betterworldclub for roadside assitance. Othervise have a great trip.
You did see the OP is planning on going in January?
Everything is different in the summer then in the middle of winter especially in the northern states and the NE US so your 20000 miles would be cake if the OP hits alot of snow / ice.
Of course summer is different than winter. No question about it. The reason for my post is: Go on trip in a car with 75K on it he will be fine.