You're totally wrong about that. Anchor babies have nothing to do with amnesty or no amnesty, but are an interpretation of the constitution that any child born on US soil, regardless of the parent's citizenship, is a US citizen. Parents could still enter the US illegally, present themselves at a hospital, and have their anchor baby delivered at taxpayer expense.
There are other anchor baby parents who arrange vacations to US, come here from Asia or other non-Latino parts of the world, have a 'US citizen' child, then return to their home country with their anchor baby. They do that just in case things become untenable in their home country in the future.
The only thing that will end the anchor baby scam is a change in how the constitution is interpreted, by the courts or through new legislation that stood up in court.
Anchor babies come with a whole host of government benefits. If it provided no benefit to illegal entrants to the country, they wouldn’t bother doing it.
“Babies born to parents in the U.S. illegally are called “anchor babies” because they automatically become citizens and immediately “anchor” their illegal families to free federal, state, and local benefits. 45% of anchor babies are born to unwed Mexican teenagers. They get on welfare immediately and can stay on welfare for life. Birthright citizenship is an irresistible magnet to get free benefits. There are about 400,000 new anchor babies born every year in the United States. 10% of all births in the U.S. are to illegal aliens. In Los Angeles, 25% of all births are anchor babies. One anchor baby is born every five minutes.” http://www.voiceforvoters.com/?cat=9