We study perturbations of one-dimensional Schr6dinger operators -(d2/dx 2) + V(x) by potentials 2 x corresponding to constant electric fields. Under such perturbations, the continuous spectrum expands to the entire real axis while the eigenvalues of the unperturbed operator disappear. The eigenvalues of the unperturbed operators turn into resonances. The main problem here is to estimate the width of these resonances. Upper bounds were given by many authors, e.g. [2, 7, 9], while lower bounds have only been obtained so far by [2, 3]. Harrell and Simon [2] obtained a lower bound for the resonance corresponding to the lowest eigenvalue of the hydrogen atom. To this end, following Schr6dinger, Oppenheimer, and Epstein, they have separated variables in parabolic coordinates, reducing the problem to a one-dimensional one, which they then transformed to the one-dimensional anharmonic oscillator for which they used the one-dimensional WKB method to derive their estimates. Harrell [ 3] used ODE arguments (in the spirit of the WKB method) to obtain general lower bounds for resonances of Schr6dinger operators in one dimension. We use ODE arguments in our study, but our approach is different from the approach of [3]. We consider general one-dimensional Schr6dinger operators and their arbitrary eigenvalues. Using elementary and rather general estimates related to the spectral deformation method, we give lower bounds for resonances corresponding to eigenvalues of the unperturbed problem.