The United States is not the only country dealing with the issue of birthright citizenship. In 2010 The Dominican Republic adopted a new constitution which ended universal birthright citizenship.
In September 2013 a Constitutional Court applied the new standard retroactively to 1930. The court ruling limited Dominican citizenship to those with at least one Dominican parent. As a result thousands of people of Haitian origin born in the Dominican Republic, unable to prove the legal status of at least one parent, were retroactively stripped of their Dominican citizenship. This decision has received considerable criticism.
Last year, Dominican Congress passed a law (see the Spanish text here) establishing a regularization process for Dominican-born children of Haitian illegal immigrants, allowing them to register as foreigners, and then after two years apply for naturalization. (There's also a separate amnesty underway for illegal immigrants born in Haiti.) However, many face the possibility of deportation due to a failure to register by the deadline set by Congress.
There are significant differences between the U.S. and Dominican debates over birthright citizenship. Despite claims to the contrary, the debate over birthright citizenship in the United States is about prospective changes – i.e., changing the citizenship procedures for the future, rather than revoking citizenship already granted, as in the Dominican Republic. What's more, while more than half the illegal population in the U.S. is from Mexico, there's more diversity than in the Dominican Republic, where virtually all those affected by the new citizenship rules are Haitian.