$1,780, if you spread it out over a week, is $250/day. That doesn't even count the gas. For that kind of money, you could drive a car or SUV (so the dogs would have space), save on gas, and have plenty left over for motels and food. If you do it during a nice time of year, you would still even have enough to buy some nice camping gear and tent camp. Plenty of campgrounds along the way that have showers etc.
And, for the record, 4-5 days isn't even that much to sightsee. I did Chicago to California, and it took me 5 days, could have done in 4 if I wasn't alone and it wasn't December. I drove an SUV and only really stopped for gas and lunch, except for the day I drove from Grand Junction to Vegas, I stopped often along the first part of that trip because of the scenery. I did the following:
Day 1: Chicago to Omaha
Day 2: Omaha to Ft Collins, CO (a bit out of the way but had family there)
Day 3: Ft Collins, CO to Grand Junction (purposely planned this day short in case of bad weather through the mountains, weather was fine though)
Day 4: Grand Junction to Las Vegas
Day 5: Las Vegas to Fresno
