The lower end canon D SLR's do not have any type of "anti-shake" built into them. Point and Shoot camera's by contrast all have something like this built in.
The auto mode with the canon will try its best to adjust the shutter speed, aperture etc. to take the photo fast enough that you don't get any shake. You can buy lenses that have "Image Stabilization" built into them, this nearly fully eliminates his problem.
I believe mose of the Nikon's have this built into the body. Correct me if i'm wrong please.
The canon (I have one) does a good job in auto mode to stop any blur, unless it's really dark out there isn't much you can do.