We modeled the low-energy electron attachment to the sugar-phosphate-sugar (SPS) molecule for investigating the single-strand break (3' C-O and 5' C-O) at the DNA backbone. In particular, we predicted the electron capture at the phosphate center. We found that 0.6 eV electron can attach to the phosphate group, and the lifetime (similar to 40-55 fs) of the resulting temporary negative ion state is more than what we found for the lifetime of the metastable species (similar to 18-20 fs) formed at the cytosine base center. We treated the two competing dissociation channels in SPS molecule, that is, both the 3' C-O and 5' C-O lesions, separately. The activation energy bather calculated for 5' C-O bond rupture is found to be less than that for 3' C-O bond dissociation. The overall low-energy electron transfer process is found to be mediated through a "shape resonance state" formed at the phosphate center.