We solve the equations of two-dimensional hydrodynamics describing a circumbinary disk accreting onto an eccentric, equal-mass binary. We compute the time rate of change of the binary semimajor axis a and eccentricity e over a continuous range of eccentricities spanning e = 0 to e = 0.9. We find that binaries with initial eccentricities e(0) less than or similar to 0.1 tend to e = 0, where the binary semimajor axis expands. All others are attracted to e approximate to 0.4, where the binary semimajor axis decays. The e approximate to 0.4 attractor is caused by a rapid change in the disk response from a nearly origin-symmetric state to a precessing asymmetric state. The state change causes the time rates of change (a) over dot and (e) over dot to steeply change sign at the same critical eccentricity resulting in an attracting solution where (a) over dot = (e) over dot = 0. This does not, however, result in a stalled, eccentric binary. The finite transition time between disk states causes the binary eccentricity to evolve beyond the attracting eccentricity in both directions resulting in oscillating orbital parameters and a drift of the semimajor axis. For the chosen disk parameters, binaries with e(0) less than or similar to 0.1 evolve toward and then oscillate around e approximate to 0.4 where they shrink in semimajor axis. Because unequal mass binaries grow toward equal mass through preferential accretion, our results are applicable to a wide range of initial binary mass ratios. Hence, these findings merit further investigations of this disk transition; understanding its dependence on disk parameters is vital for determining the fate of binaries undergoing orbital evolution with a circumbinary disk.