There is not currently any specific "pathway to citizenship" designed for people who are currently in the country illegally. They would have to qualify for a green card on the same basis as anyone else, then apply for citizenship after that.
However, they often are not eligible to do so because of their illegal prescence. If one has been in the US illegally, as an adult, for more than 180 days, they have a three-year ban. After one year it becomes a 10-year ban. This applies to both visiting and immigration. They have to return home (or another country) to serve the ban before getting a visa to return.
One notable exception to this rule is marrying a US citizen, but only if the initial entry was legal (i.e. visa overstay, not border jumping). Being a parent of a US citizen also works, but the child has to be 21 first. Being a parent of a US citizen under 21 has no immigration benefits.
I'm almost certain that the reason is to prevent people from entering the US as a visitor when pregnant, having a child, and then immediately being able to have the one-day old child petition for the parents. Or having a child while facing removal proceedings. As it stands currently, the child still becomes a citizen immediately, but cannot petition the parents until they are an adult.
If the rule stays, then US citizen children can be left with no adults in their life legally able to raise them in the US. On the other hand, if having a child in the US becomes an automatic ticket to citizenship, there will be a significant increase in children being born for this reason only that may be neglected, and people who want to overstay and are willing to have a child are basically guaranteed the ability to do so.
Another side effect if removed would be that the US border folks may be unwilling to admit pregnant visitors even with very legitimate reasons, because they know there is nothing to stop them from obtaining a green card if desired.
edit to clarify: even without this rule, you have to have entered legally, so just illegally crossing and immediately having a child wouldn't work--you would have to enter as a tourist or otherwise.
The idea is that adults can sponsor their parents for a green card but children cannot. Of course it makes absolutely no sense given the disruption to US citizen children's lives if their parents are deported, but US immigration generally is quite cruel if you're on the margins.
I think parents of US citizen children cannot be deported for that exact reason: it would leave the child without a parent. That's why they are called "anchor babies".
But of course if they leave the US willingly (e.g. traveling to their home country) they will be banned from ever coming back.
> I think parents of US citizen children cannot be deported for that exact reason: it would leave the child without a parent. That's why they are called "anchor babies".
Yes, they can be deported. This has affected me personally and other members of my extended family.
However, they often are not eligible to do so because of their illegal prescence. If one has been in the US illegally, as an adult, for more than 180 days, they have a three-year ban. After one year it becomes a 10-year ban. This applies to both visiting and immigration. They have to return home (or another country) to serve the ban before getting a visa to return.
One notable exception to this rule is marrying a US citizen, but only if the initial entry was legal (i.e. visa overstay, not border jumping). Being a parent of a US citizen also works, but the child has to be 21 first. Being a parent of a US citizen under 21 has no immigration benefits.