Standard statistical methods assuming the exchangeability of units between treatment groups can yield biased treatment effect estimates if the assumption does not hold. Existing methods evaluate the sensitivity of treatment effect estimates to non-exchangeability due to unobserved confounders only. We propose an index of sensitivity to non-exchangeability (ISENSE). Unlike many existing methods, it does not require any assumptions regarding the distribution or number of unmeasured confounders, and it can handle both unmeasured confounders and reverse causality. ISENSE is a local sensitivity method based on a Taylor-series approximation to the non-exchangeability likelihood, evaluated at the parameter estimates under exchangeability. One can interpret ISENSE intuitively through the MinNE statistic, which captures the minimum non-exchangeability to change the results. We evaluate ISENSE using simulation studies and illustrate its use with an example using administrative data.