For the moment, you don't need a passport to cross the Canada-US border. The best thing to do, though, is to make sure you have proof of identity and proof of citizenship. A driver's license alone is not proof of citizenship (you don't have to be a US citizen to get a driver's license). A driver's license along with a copy of your birth certificate would be much better.
It's not for getting into Canada that you really need the passport, its for getting back into the US. I always take mine when I travel now, and last time I drove across the border the US customs people really hasseled the car in front of me with US plates when the driver couldn't prove US citizenship. And no, a driver's liscence doesn't prove citizenship, just residency.
When they finally finished with that car, I was through with just a few questions.