With regard to FUD on the part of the masses driving legislation, I suppose it's an intrinsic part of democracy. Which implies the following:
The vast majority of those satisfied by the status quo are the uninformed members of the public. On the other hand, the highly educated and those driving the economy are strong proponents of leniency in immigration, as evident by the frequent discussions on popular forums such as leading publications and HN.
The average American believes that more opportunities are made available to them, regardless of whether they're qualified, if they stop immigrants from coming and stealing their jobs. Which I suppose is a reasonable conclusion for an uninformed person to reach.
The solution? Inform the public, for after all, the US is a democracy, and it's in their hands to change the system. Explain how immigration is essential to the development and progress of economies, educate people on the implications of immigration.
PS: I would be interested to learn if there are any non-profits that run campaigns that aim to educate and inform the public.