I wouldn't count on driving a car from California to Connecticut this time of year. In December, there's a pretty good likelihood of running into snow and/or frigid temperatures for much of the trip, which includes the snow belt of the Great Lakes region. What do you plan to do if there is a big blizzard? Would you be able hunker down for a few days, or would this spoil the entire trip? What if the temperatures are really cold (say 0 F); would you continue, even given the low traction of your tires? You would undoubtedly be better off swapping for winter tires for this trip (and, with that many miles to drive, it would be worth it). For more info about choices for the NSX, see
http://www.nsxprime.com/FAQ/TireWheel/snowtirechain.htm
If your time schedule were extremely flexible - and could postpone your trip by several days or a week if you encountered snow - you might be able to get away with it. But you're taking a big chance that you won't be able to drive on some of the days you're planning.
For more information about the climate in the Great Lakes region, check out
http://mcc.sws.uiuc.edu/Summary/index.html For example, here are the statistics for the month of December for Chicago:
Chicago
-------
Average high 34.0 degrees F
Average low 19.1 degrees F
Average 11 days in December with high temp below 32 degrees F
Average 2.3 days in December with low temp below zero degrees F
Average snowfall 8.8 inches
Cross-country trips are great, at the right time of year. In winter, across the northern part of the country, I would ship the car, no question.