I am in urgent need of a response here. I have no place to stay and hotels in the states are rather expensive. All I have is my trusty minivan. Is sleeping in a van generally a good idea to save cash? And if so, where are some nice places to pull off and sleep? Are rest stops good ideas, or are they too dangerous?

As the road-trip king, I gotta say, for the most part, sleeping in yer van is not a bad thing...

Rest areas are a mixed bag of nuts, they're generally well patrolled by the highway patrol, but that's cause they draw trouble in some areas (stay away from the ones near metropolitan areas) and they are also designed for short stays (usually 6 hours or less) There are sufficient areas to camp out near the roads (national forests, desert turn offs etc) that aren't too bad, and if you're gonna stay in an area for a while, there are usually low cost campgrounds (both private and run by the forest service) that have showers, etc and are usually a good alternative to parking alongside the road somewhere...

By the same token, look for national forests, parks etc, where you can often stay for a day or two for a minimal charge, and often can overnight in unimproved areas with no charge at all (check with the local ranger station if you wanna make sure you're staying kosher)

I agree with Will. Find National Forests and such. Avoid rest areas for sure!

It's best to find extremely cheap or free scenic areas to crash for the night like national parks and such, but otherwise, there are other options too.
Wal-Marts are usually RV friendly, most stores actually encourage RVers to park overnight. While I understand your mini-van isn't an RV, I'm sure you'd be received relatively in the same fashion. Also, truck stops frequently have an overnight RV area. Rest stops are indeed the least safe option.

I've done the "pull onto a dirt road and drive into the woods" thing more than once. The only way I can sleep in my pathfinder is with the tailgate open so I make sure I am off the beaten path before i curl up at night.

I've had to sleep in a rest stop before and it wasn't too bad. I was kind of scared, but everything was fine. Some states (Mississippi) have 24/hour security in their rest stops.

Also consider gas stations that double as trucker stops - you know with the super huge parking lots and stuff.

Also pulled off in a suburb of Milwaukee and slept in a bank parking lot after Summer Fest one year. Probably not legal, but we got some sleep and drove much safer.