Or less. Try 9mpg. I think you need to rethink your distance. 4000 miles in 14 days = 285 miles/day. That leaves almost no time for stopping. Have you ever driven a motorhome? Its not like driving a car. Everything takes longer than you think and 350 miles is a long haul for a lot of people. Not saying you can't do it, but I have experience towing a trailer and it will wear you out if you're driving to drive, drive, drive every day. And what's the point? You don't want to see America from the windows of your RV, do you?
We actually did a cross-country trip with our kids 3 years ago. 6000 miles in 60 days. Some days we drove a lot, some days we didn't even move. THe longest we ever drove was 450 miles in one day and it was exhausting. We had to stop for 3 days to recover. Coming back from Yellowstone to Atlanta took 5 days of hard driving--we HAD to be home by a certain date. By the time we got home we were totally spent. (of course, after a few days rest we were raring to go again

)
I would suggest that you plan a loop trip. From Connecticut you might go up to Maine, see Acadia NP, eat some lobster, or go through New York, see Niagara Falls and Lake Placid. Or head to Lancaster, PA, Philly, or go over to Gettysburg. Head down to Williamsburg, VA and over to the Outer Banks. But not all these places in a 2wk period. Think of this not as your Big Trip, but your First Trip. Once you get the RV bug you'll never be the same.
I agree with all of this. I full-time in an RV with my father. He's retired on disability, I'm a travel writer specializing in disabled adventure travel, and he's my guinea pig

We've been full-timing for about five years now, and really hitting it hard for the past year. We try to average around 200-300 miles per day, but then tend to stay in each area for at least a week, often 2-3 weeks. We like to get to know an area, explore the history and culture, and meet the locals.
We recently did 450 miles in a day, from Williamsburg, VA to Yemassee, SC, an hour south of Charleston. Like minkydog, we we were on a tight schedule. The 7 hour (mapquest estimated) drive took closer to 10 hours, and we were both exhausted and miserable by the end.
Everything just takes longer with an RV, from finding a gas station that'll accommodate an oversized vehicle to hiking in to a restaurant for a lunch stop (no drive-thrus and no parking close, the RV won't fit). When you arrive, you still have to set up the RV--detach your tow/towed vehicle, plug into electricity/water/sewer, arrange the beds if anyone's sleeping on a convertible couch or dinette, unpack things. Then in the morning, you have to stow everything away for travel, disconnect your utilities, dump your black tank. Plan on AT LEAST an hour at night and another hour in the morning every time you move, more if you have a lot of stuff, a satellite dish or don't know exactly what you're doing.
That said, RVing is a fabulous way to see the country. You just have to slow down and avoid the temptation to see and do it all. Base camping works extremely well for us. Figure out where you want to be, park the RV in the middle and take your car to see things around the area. We tend to do sightseeing within a one to two hour driving radius around the campsite.
I like the different trip suggestions that minkydog made. My personal vote is for Williamsburg, VA. We went for three weeks this summer and ended up staying for two months. Just so much history and culture in the area, as well as Busch Gardens, Water Country, Ripley's...it's a fabulous place to take kids, and interesting for adults as well. Another advantage is that there are several reasonably-priced RV parks centrally located within a few miles of everything. In some areas, you'll find that the RV parks are 20-30 miles from civilization.