Here in the real world, every American I know knows that the only way for "normal" (non-rich, non-connected, non-extraordinary) person to legally immigrate is to marry an American citizen and have them sponsor you. Literally everyone knows the average "illegal immigrant" living in the US isn't eligible for citizenship and couldn't obtain citizenship legally. Exactly zero people think that any (let alone most) "illegal immigrants" could have just "followed the rules" and been able to live here legally. The reason they are "illegal immigrants" is because there's no legal way, other than marrying an American.
A lot of people would prefer if even family sponsorships didn't exist. Many people think of that as "gaming the system" because they allow "average" people to be immigrants. I assume Republicans want to get rid of this.