We have explored the spin liquid state in Tb₂Ti₂O₇ with vibrating-coil magnetometry down to ∼0.04K under magnetic fields up to 5 T. We observe magnetic history dependence below T* ∼ 0.2K reminiscent of the classical spin ice systems Ho₂Ti₂O₇ and Dy₂Ti₂O₇. The magnetic phase diagram inferred from the magnetization is essentially isotropic, without evidence of magnetization plateaus as anticipated for so-called quantum spin ice, predicted theoretically for [111] when quantum fluctuations renormalize the interactions. Instead, the magnetization for T ≪ T* agrees semiquantitatively with the predictions of "all-in-all-out" (AIAO) antiferromagnetism. Taken together, this suggests that the spin liquid state in Tb₂Ti₂O₇ is akin to an incipient AIAO antiferromagnet.