My new born baby could have a heart murmur, how serious is that?

It is uncertain . A murmur is an extra sound. The causes are many and range from normal sounds to mild defects that do not require treatment, to serious problems that may require surgery. A complete evaluation is necessary to know for sure.
Depends on the cause. A murmur is a type of heart sound the doctor can hear with a stethoscope. Whether nor not a murmur is a birth defect depends on the cause of the sound. If the sound is caused by incorrectly formed arteries, veins, or heart parts, then the problem is a birth defect. On the other hand, many normal children have murmurs but no defects (the murmurs are probably just from the flow of the blood).