C-SPAN has the video of Obama's address and signing to overturn President Bush's restrictions on the federal funding of embryonic stem cell research.
During his address (at around 5:15), Obama said "we will ensure that our government never opens the door to the use of cloning for human reproduction. It is dangerous, profoundly wrong, and has no place in our society, or any society."
By "reproduction" Obama seems to mean bringing a cloned human child to birth. It's not really accurate terminology since all human cloning (regardless of whether the clone is implanted or killed) is reproductive.
This is the same Barack Obama who co-sponsored S.B. 1520. S.B. 1520 was called the "Human Cloning Ban Act of 2005" but didn't do anything to ban human cloning. The only thing it banned was the implantation of human clones. It used a unscientific and intentional misleading definition of "human cloning" to act like it was banning human cloning when it was only banning the implantation of a human clone.
So Obama's position on human cloning is that it is perfectly alright to use cloning to create cloned human embryos as long as they are killed for their stem cells but that it dangerous, profoundly wrong and there is no place in our society for implanting human clones.