If you have trouble pushing or pulling short putts, you're probably stabbing at the ball rather than stroking it. A good putter's backstroke and follow-through should be like a pendulum roughly equal on both sides. When you take the club back too far and decelerate into impact (that is, when you bring your stroke to an abrupt end), you often open or close the face as it nears the ball.
One way to tell if you're stabbing at putts is to place a dime on the back of your putter and make your normal stroke. If you're truly stroking your putts, the dime will stay on the putter throughout your stroke, no matter how far back and through you take the putter. If you're stabbing instead of stroking, however, the dime will slide off the back of your club as soon as you transition from the backstroke to the forward stroke.