We present lower bounds on the error probability of turbo codes under maximum likelihood (ML) decoding. We focus on additive white Gaussian noise (AWGN) channels, and consider both ensembles of codes with uniform interleaving and specific codes with fixed interleavers. To this end, we advocate the use of second order distance spectrum which considers pairs of codewords, and enumerates individual codeword weights along with the correlation values between them.  We develop a way to compute the second order distance spectrum for convolutional codes and for turbo codes under uniform interleaving. Our results show that proper restriction of the error events together with the approach of using the exact second order distance spectrum result in good error rate lower bounds.