i.e. Anchor babies. This is a matter in dispute yet to be settled, I predict not in my lifetime, maybe never.
Whatever controversy there may be as to whether the 14th Amendment requires babies born to two illegal aliens to be citizens, the statutes in force today (and back in 1961) clearly provide that they are. Besides which, no one disputes that the 14th Amendment would give citizenship to a child born on U.S. soil to a citizen-mother (or even to an alien mother who is lawfully in the country). So, assuming Obama was actually born in Hawaii, he is a natural-born citizen under any possible view of the law.