While I have no problem with Congress appropriating money to help legitimate "first responders" in a case like this, there is an angle to the whole 9/11 aftermath in NYC that doesn't get a lot of attention.
For one thing, many of the people experiencing these health problems weren't the initial firefighters and police personnel on the scene on 9/11, but were there for months afterward. There was no urgency to the work these NYC personnel were doing, and after the shock of the attack wore off the whole thing rapidly declined into an overtime scam for municipal workers and unionized construction workers. A contractor I know had volunteered to have his crews and equipment help with the cleanup at no cost, but he was told he could not help because his workers were not represented by a union.
The firefighters got into the act by getting the NYC government to agree that FDNY "honor guards" would be on the scene at all times during the cleanup -- to carry away the remains of any firefighters recovered at the scene. You can go to the 9/11 Memorial website today and find dozens of images like this showing this type of scene:
Keep in mind that this wasn't even close to a rescue operation anymore. There wasn't even a need to have any of these first responders on the scene at all. Most of the photos shown here were taken in the spring of 2002.
I'm sure this ain't politically popular for me to say this, but if I were a member of Congress I wouldn't vote to authorize one more penny of Federal money for any "victims compensation fund" anymore.