jacamille:
In order for any spring to flow, it needs to be fed from an aquifer that is higher than the spring outlet -- to provide the hydraulic "head." However, the aquifer could be many miles away, or it could be just your local groundwater level. If you just punctured the "cap" on the local groundwater level, it may just rise to a point and then level off. If the spring is being fed by an aquifer some distance away and higher than the top of your dam, you could reach an overflow situation.
Any good pond design should include an overflow pipe and/or a well designed spillway to allow excess water to escape without washing out your dam. Otherwise, it will probably just be a matter of time until you get a "gully washer" thunderstorm or other big rain/snowmelt combination that fills the pond to the top of the dam. If you don't have a spillway designed to allow the excess water out without washing out the dam, you will end up with a mudhole instead of a pond.
I am not an engineer, but in my job I had to select sites for stock watering ponds (called "tanks", or "tanques" in the Southwest). The ones with poorly designed spillways and no overflow pipes eventually wash out and the cost and time spent for construction was wasted. If the volume of water held by the pond is significant, they can also cause downstream flooding problems when the dam washes out. Doesn't sound like your pond is big enough for that to be a concern.
Your local county extension agent or the Natural Resource Conservation Service (formerly the Soil Conservation Service) can probably provide advice and specifications for spillway construction.
Good luck. Just wish I had a spring on my property so I would have your problem.