Assuming you're traveling on Interstate highways and avoiding major cities, I've found 700 miles to be pretty easy with the added benefit of time for an actual restaurant meal at the end of the day. 800, 900 and 1,000 mile days are possible but become progressively much more difficult and perhaps more dangerous. Unless you have a backup driver or are young, 1,000 mile days are really pushing it.
I've done these drives in all kinds of cars; your new Honda should be a great choice. Assuming the car is reasonably comfortable and quiet, there are only three situations in my experience where vehicle choice makes a big difference:
1) High-profile vehicles (vans, SUVs) are no fun in high winds, particularly as experienced in the western states. Battling winds makes a long day much longer.
2) Mountain driving in underpowered/heavily loaded vehicles is unpleasant.
3) AWD or not, tread depth makes a huge difference in winter driving conditions.
Enjoy your travels!