We show the shortest vector problem in the l_2 norm is NP-hard (for randomized reductions) to approximate within any constant factor less than sqrt(2). We also give a deterministic reduction under a reasonable number theoretic conjecture. Analogous results hold in any l_p norm (p>=1). In proving our NP-hardness result, we give an alternative construction satisfying Ajtai's probabilistic variant of Sauer's lemma, that greatly simplifies Ajtai's original proof.