What happens if the sinoatrial node starts to speed up or slow down, for a long period time?
The sinoatrial node (SA node), located in the right atrium of the heart serves as the hearts "normal" pacemaker. This refers to the conduction pathway of the myocardium. The heart is a muscle and just like other muscles must receive a stimulus to work/beat.
The conduction pathway is the normal way or route that the heart receives the stimulus to beat. The pathway consists of the SA node, AV node, bundle of His, purkinje fibers, left and right bundle branches.
The SA node can speed up or slow down depending on external or internal influences. If it speeds up, the heart rate would increase but it would still be a sinus rhythm, this would be called sinus tachycardia. Technically, the SA node can slow down but it depends on how slow you are talking about. If the node was damaged by disease or trauma, then another area would take over the business of propagating a heart beat.
For example, say the SA node was damaged by trauma, the AV node would then take over, if the AV node was damaged, then the bundle of His would take over, if the bundle was damaged, then one of the bundle branches would control.
The conduction system/pathway is like insurance for the heart. When one area can't function, another takes over. If the SA node sped up and remained fast for long periods of time (real question is how fast), this would have adverse affects on the rest of the body. Each node/area has an inherent rate. The rate for the SA node is 60-100 bpm. If the heart rate was for example, 108, that is "abnormal" but it is not a problem. If the heart rate fell below 60 bpm, you would have sinus bradycardia.