The narrator's comments are a bit off and don't really speak to the fundamental reason why this typical liberal inability to understand Scripture or Christianity is wrong. Deuteronomy isn't what gave us the 10 commandments it only repeated them but anyhow...
Part of the problem is that Obama has been raised in Protestant Christianity which is, without mincing words, an offshoot of true-Christian doctrine.. i.e. it is heretical. He is treating Christianity here as if it were a 'religion of the book' as Islam is for example and authentic Christianity certainly is not a 'religion of the book'.
There is a professor at UNC Charlotte who opens his course on Paul with the line "Paul affected Christianity more than Jesus did" and the same sort of straw man attack is happening. I am willing to bet that this professors' primary exposure to Christianity is a Protestant one in which entire Bible is read through Pauline goggles instead of reading Paul along with the rest of the Scripture. His reasons for thinking that Paul has such enormous influence on Christianity is that his idea of Christianity is skewed by a sect (and one that represents a small historic minority). So this is one problem I see here, identifying "Protestantism" with true Christianity (not to say Protestants aren't Christian) when if he understood authentic Christian doctrine, his ideas wouldn't even get off the ground.
But in case those silly ideas do get off the ground, they are easily shot down. Obama is making the same fundamental error as I made when I was an uneducated teenager and the same one Martin Sheen arrogantly makes in this clip:
Neither Obama or Sheen understand that the OT Law was written for a specific people at a specific time. They make several errors. First they think that we either have to follow all the laws exactly until this day or none. Second, they think that mentioning a practice that occurs without explicitly condemning it is the same as condoning it. (Because the Scriptures mandate things to do with slaves such as treat them humanely etc... without condemning slavery necessarily means that Scripture condones it in their minds...) Third, they assume that since arbitration is required, it must be up to the individual instead of the Church. The voice of the Church is left out of the equation in both of these videos.
Neither of them understand the difference between apodictic and didactic laws. Apodictic laws are those which are necessarily true and thus true for all ages (do not commit adultery for example) and thus correspond to the natural law. Didactic laws are intended to instruct and are not always necessary under all circumstances (do not mix types of threads for example). Now if Martin Sheen isn't clever enough to figure out that (do not sleep with a man as with a woman) falls under the category of Apodictic law and is a heinous violation of natural law, then the Church has an unambiguous voice to tell him so. And if Obama isn't so spiritually keen to know that slavery is against Christian morality and that stoning your children is not part of God's plan for parents, then... again, the Church is here to tell him so.