Generative artificial intelligence (AI) is expected to transform work, but less is known about how firms reorganize labor demand as the technology diffuses. Existing research has largely focused on which occupations are exposed to AI or whether exposed jobs decline. We extend this debate by examining whether firms adjust by changing where they hire, what jobs contain, or both. Using a nationwide dataset of job postings in the United States, covering all sectors of the economy, we construct a dynamic, posting-level measure of generative AI exposure with a two-stage large language model pipeline. The pipeline identifies the tasks described in each posting and classifies the extent to which generative AI can perform or assist them. We then decompose changes in aggregate exposure into two margins: reallocation of demand across jobs and redesign of tasks within jobs. We document three main findings. First, generative AI exposure is dynamic rather than fixed, changing substantially over time. Second, labor demand adjusts through both margins. Hiring reallocation explains the largest share of the aggregate decline in exposure, accounting for 52% on average, while within-job redesign becomes increasingly important, accounting for 39.5%. A complementary Oaxaca-Blinder decomposition shows that shifts in occupational composition account for about 90% of the exposure change attributable to observable job characteristics. Third, adjustment differs across the job ladder. Senior jobs adjust earlier and mainly through reallocation, whereas junior jobs adjust through a broader mix of reallocation, redesign, and their interaction. These findings suggest that labor-market adjustment to generative AI is a process of organizational reconfiguration, in which firms reshape both hiring demand and the task architecture of work.