There are certain parts of ADA which most everyone agrees with (blind people should be allowed to bring seeing-eye dogs everywhere; people should not actively discriminate against persons with disabilities because they disapprove of them; if you building a brand new medical center, it should have wheelchair ramps and elevators).
The controversy is about where ADA draws the line, especially when it comes to retrofitting old construction. The enforcers of ADA impose overly strict rules. For example, if the buttons on your elevator are 2" too high, then you must lower the buttons right-now, or else they will close your building. The ADA is indiscriminate in the use-case of buildings; you can operate a kickboxing gym and be required to spend $$,$$$ to rebuild your bathrooms to make them ADA complaint, even through nobody in a wheelchair will probably ever use that bathroom in your lifetime. The ADA take an extreme view on the meaning of 'accessibility'. Your swimming pool cannot have a portable pool-life which the lifeguards roll out from the shed on the occasions when it is needed, and instead you have to install a fixed pool lift because it's somehow not 'dignified' for a person in a wheelchair to have to ask the lifeguard to wheel it out.
The epitome of the lunacy of ADA was in the Supreme Court case Tennessee v. Lane, where a paraplegic (who for the record was not a disabled war vet, but someone who crippled himself in an accident where he himself was DWI) was back in court on another traffic charge. The courthouse did not have an elevator, so the judge offered to move the hearing downstairs from the 2nd floor courtroom. Lane refused. The guards offered to push his wheelchair up the steps. Lane again refused. Finally Lane hoisted himself up the stairs on his hands and butt. At the next hearing, Lane refused everything and wouldn't attend the hearing, and the court found him in contempt. There was a lawsuit, and eventually the Supreme Court sided with Lane. The ridiculousness of the decision is that if the judge was agreeable to holding the hearing in a separate room, isn't that reasonable enough? And if the defendant showed that he could go up the stairs on his hands and butt, then doesn't that action establish that the 2nd floor courtroom was 'accessible' to him? No, says the ADA. It enforces a weird concept of 'dignity' on the country where it says the disabled need to be accomodated so that they do not 'seem' disabled, even though they are.
Again, there's little controversy that in many cases (like the new construction of large public buildings) the ADA works out fine. But the opposition stems from the many other cases where strict ADA compliance costs of a lot of money bringing a very minor benefit very infrequently to very few people.
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