New FLAMES/GIRAFFE public data allows to revisit the issue of the origin of the supersonic turbulence inferred in the ionized gas of Giant HII Regions using the prototypical 30 Doradus nebula in the LMC as a guide . We find that the velocity width of the integrated H \alpha line-profile of 30 Doradus can only be explained by the motion of macroscopic parcels of gas driven by the gravitational potential of the stars and gas with a significant contribution of stellar winds . At all positions within the nebula we find that an additional very broad ( \sigma = 40 - 50 { km~ { } s ^ { -1 } } ) unresolved component is required to fit the extended wings of the profiles . We find that fitting two Gaussian components to the integrated emission-line profiles provides a robust way of separating the contributions of stellar winds and gravity . Assuming an effective radius of 10pc for the nebula we thus infer a dynamical mass of \sim 10 ^ { 6 } { M _ { \odot } } for 30Dor . Our analysis of published observations of the second largest Giant HII Region in the Local Group , NGC 604 , shows that our results for 30 Doradus apply to GHR as a class .