Giving up current pets wasn't the point of HR669 and is not going to be the point of any future bill in the matter. It was meant to limit the trade, transport, and sale of such creatures (essentially grandfathering the law in).
Potential future bills may require the purchase of a permit to buy potentially invasive species (which, as with HR669, will not include most aquarium fish. They just don't fit the invasive profile). The proceeds from these permits would then cover efforts to control invasive species already in the wild, as well as educate the public to avoid further introductions.
As a side note, I went for a walk with my mom around a swampy lake in our city, and noticed that the snails (I believe the ones called "Japanese trapdoor snails" at Liveaquaria) have grown huge and extremely numerous. There's also a
goldfish population in the lake. I'm sure the herons and egrets love the goldies, but the native fish are gone, and the snails are making short work of all but one or two of the shore grasses.
I really wish people just wouldn't dump/release their unwanted pets. We wouldn't have to have these discussions, then, and we'd be able to focus on how wonderful our fishies are.
Second Edit: And don't get me started on the countries destroying pigs to curtail H1N1... It's a waste and will not stem the spread of infection in the least. The virus is the human virus, and merely has a bit of swine flu and avian flu material in it. It's being spread by humans, not by animals.