You can reject a disabled employee's accommodation request (or refuse to hire a person) if the individual isn't able to perform the "essential functions" of the job, even with an accommodation. But many ADA failure-to-accommodate lawsuits hinge on which tasks are considered essential.
For that reason, it's important to clearly define the essential functions in each job description. To make the decision, focus on the result of the function, rather than the manner in which it's performed.
Before you reject an accommodation request, consider the impact it would have on disabled employees. Prepare to justify those changes with solid evidence. In the following case, Hershey couldn't prove that its job-rotation system was essential to an employee's job.
Recent case: Janet Turner, a production worker on Hershey's Peppermint Pattie line, requested accommodations after back surgery. Hershey placed her on a light-duty candy-shaker line, which allowed her to sit.
But the factory, in an effort to reduce repetitive-stress injuries, soon began a system of rotating workers through different production lines every hour. Turner asked to be excluded from the rotation, but Hershey refused, saying the job-rotation was an essential function for all candy shakers.
She sued, and the court sent her case to trial, ordering Hershey to show why exempting Turner from the job rotation was either an undue hardship or a threat to others. (Turner v. Hershey Chocolate USA, No 04-4674, 3rd Cir., 2006)
Final tip: Just because you make one accommodation, doesn't mean you get a free no-liability pass later. When a job changes, so may the accommodation.