Though a few have actually had success in the past doing this method, now days it's pretty much a big risk and you are seriously risking issues comming back into the US, let alone even getting into Canada with that. You need to check the INS websites for Canada and the US to see what constitutes as proper ID to get across both borders.
If you are flying they will not even let you board without a passport. Driving you can do it without a passport, but doubtful just the Nat Cert will do it, you'll probably need photo ID's and other documents and not to mention a lot of extra time in secondary inspection...