That's actually pretty ambitious, all things considered. Having a reliable car is key, and though it's a really great way to see a huge country like Canada, it's also got the potential to turn into the worst nightmare you've ever seen!
That said, gas (in the states) runs about $3.00 a gallon, (in Canada, they're about 30% more). You're looking at a trip of about 2500 miles, give or take. If it's an efficient car, you'll average 25-30 miles per gallon (depending on how you drive, terrain, air conditioner, etc.)
Given that, the trip alone is about $400 Canadian (counting the exchange and higher gas prices) in gas.
Without pushing yourself too hard, and leaving time to stop and take pictures etc., you can expect to make 300 miles a day. (you can push much harder and make more, but then you're doing nothing but driving) so look at 9 days of travel, barring incident (the bad car scenario)
Motels in rural areas can be cheaper, and if you have a tent, you can car camp fairly cheaply, so $100 a day for food and lodging would be generous. I don't recommend sleeping in your car too much, because it's simply not comfortable.
I've taken several cross-country trips in the U.S. quite successfully by car, and it's quite enjoyable. The important thing is to plan ahead on your route, so that you have a good idea where you're going to stop, and you can decide what you'd like to see along the way (there's plenty to see if you know it's there, but most of it is often a short detour off the main road away)
Don't get all wrapped up in your schedule (remember National Lampoon's Vacation
? or you'll suck all the enjoyment out of the trip... there's just too many times that I've spent more than my allotted time in one spot, and I enjoyed every minute of it!
Finding someone else going on the road-trip is tough, cause people simply don't like to travel that way much anymore...
Good luck with your trip!