A leading dark matter candidate is a Weakly Interacting Massive Particle (WIMP). The observed dark matter abundance can be naturally obtained through freezeout of the thermal annihilation rate. The defining feature of a thermal WIMP is that its total annihilation cross section is specified through the rate ~ 3 x 10^-26 cm^3/s, inversely proportional to the dark matter density. Searches for dark matter annihilation products have set strong limits in certain cases, requiring that the dark matter mass be greater than around 100 GeV if annihilation proceed solely to b quarks (Fermi), τ leptons (Fermi), or electrons (AMS). We construct the first limits on the total annihilation cross section, showing that allowed combinations of the annihilation-channel branching ratios considerably weaken these limits. We will show that GeV-mass thermal WIMPs have not yet been adequately tested, and outline ways forward.