We study theoretically the dynamics of film thinning under the action of an attractive surface force near the point of a jump instability. Our approach is illustrated by modeling van der Waals and hydrophobic attractive forces. The main result is that with the hydrophobic force law reported previously it is often impossible to establish the jump separation with any certainty. The surfaces instead approach slowly from a distance which is much larger than the point where an actual jump is expected. We conclude that an attractive force measured by the static jump technique is overestimated, and we formulate principles of a new dynamic jump method. The use of this new technique would permit direct measurements of attractive forces at separations below the static jump distance down to contact of the surfaces.