To me, the issues with migrants and illegal immigrants have everything to do with crime and competition for jobs, the issues that, it appears, Republicans have been emphasizing. But it's interesting that, at least according to this poll, many folks appear stuck on petty resentment. We are a prosperous and generous nation, and I have no objection to extending social programs to migrants who are here lawfully; indeed, taking care of the sick in doctors' offices rather than emergency rooms improves care for all of us.
To me, the linchpin isn't taking the "perks" away, but rather making the conditions more difficult for employers to hire those not here legally. Since most come here, once sanctuary is achieved, for opportunity, the ability to work should be the most precious commodity that America affords. If employers are hit hard for hiring illegals, the impact will ultimately be that folks will have greater incentive to get and keep that credential to work.