Low-level drug resistance in noncanonical pathways can constitute steppingstones toward acquisition of high-level on-target resistance mutations in the clinic. To capture these intermediate steps in Mycobacterium abscessus (Mab), we performed classic mutant selection experiments with moxifloxacin at twofold its minimum inhibitory concentration (MIC) on solid medium. We found that low-level resistance emerged reproducibly as loss-of-function mutations in RshA (MAB_3542c), an anti-sigma factor that negatively regulates activity of SigH, which orchestrates a response to oxidative stress in mycobacteria. Since oxidative stress is generated in response to many antibiotics, we went on to show that deletion of rshA confers low to moderate resistance-by measure of MIC-to a dozen agents recommended or evaluated for the treatment of Mab pulmonary infections. Interestingly, this moderate resistance was associated with a wide range of drug tolerance, up to 1,000-fold increased survival of a ΔrshA Mab mutant upon exposure to several β-lactams and DNA gyrase inhibitors. Consistent with the putative involvement of the SigH regulon, we showed that addition of the transcription inhibitor rifabutin (RBT) abrogated the high-tolerance phenotype of ΔrshA to representatives of the β-lactam and DNA gyrase inhibitor classes. In a survey of 10,000 whole Mab genome sequences, we identified several loss-of-function mutations in rshA as well as non-synonymous polymorphisms in two cysteine residues critical for interactions with SigH. Thus, the multidrug multiform resistance phenotype we have uncovered may not only constitute a step toward canonical resistance acquisition during treatment but also contribute directly to treatment failure.