Generally speaking, they will not be able to get a green card until the child reaches the age of 19 or 21 (can't remember exactly) and can file an 1-130 for their parent. Needles to say, this is one of the longest ways to get a green card. Some people say that this is why people come to the U.S., but a 20 plus year wait doesn't seem very attractive to me.
It's 21 years. And I agree: waiting for your baby to be 21 years old so you can get your permanent resident alien visa ("green card") is hardly worth it. But, believe it or not, that's the only hope to get a visa for millions of illegal immigrants right now other than marriage to an American citizen.