That drive (I'm assuming you are in Sioux Falls) to Boise is just under 21 hours if you average about 67 mph on the interstate. The cost of the trip is about $85 each way if you average $1.60 per gallon and 27 mpg. You can fairly easily find hotels that are not really all that bad for $25-$30 a night in just about any town.
In the last couple of months, I've driven east coast to west coast twice, north border to south border three times, and halfway across the country once (don't ask, it's a long story). I averaged 67 mph including stops and saw lots of cheap hotels (and stayed in a few of them) that really weren't too terrible. Even slept in the car a couple of nights. Stayed at friend's and relative's places on other nights.
So...it shouldn't cost you anywhere near $1000, probably more like $300. Less if you stay in campgrounds and less still if you sleep in your car or at friend's or relative's places. If I were you, and really tight on money, I'd drive about 16 hours straight or so, sleep for a few hours at a rest stop, and finish out the drive when I wake up. Probably not the safest advice, but it's what I did pretty regularly. You can make your trip on the cheap, it's simply a question of how much pain you want to put up with.
