Every legal US Resident or US Citizen who paid taxes regularly should be able to sponsor his immediate family (parents and siblings).
A limit can be set to "up to five relatives in a five year period" and requiring a sponsor to cover all living and medical expenses in the first five years after arrival. This would be similar to a "trial period" for the Green Card obtained through marriage.
Furthermore, every legal US Resident or US Citizen should be able to sponsor any person of their choice who can contribute to the US economy. Similar to family sponsorship, a sponsor would have to cover all living and medical expenses for the period of 1-2 years since the person arriving in the US would be expected to find employment or start a business.