No, he did not. That is an internet myth, spread by certain
anti-abortion groups. First, the president cannot pass laws-- only
congress does that. And no laws that allow late term abortion on
demand were passed by this congress. However, there remains a law
that does permit late term abortion under certain circumstances: if
the life or health of the mother is in danger, or if the pregnancy
was the result of rape or incest, abortion (even late term
abortion) may be medically necessary. That law existed before
President Obama, and at this point, there is no effort from
congress to change it.