Our problem doesn't really seem like a lack of encouragement for immigration. We have plenty of people trying to come here, we either don't want the people attempting to come or don't want immigration at scale at all.
Social programs and entitlements are really all the encouragement needed for immigration, as long as you're legally allowed to immigrate and get a job at all. Is the question really how do we encourage the "right" kind of immigrants for the skills or roles we want to expand?