[
](Slow jam - Wikipedia)
To use it as a verb would be akin to telling a band to jam, except you want the jam to be in an R&B vein.
Which (to me) makes absolutely no sense in the context of “Obama slow jams the news.”
Would “Obama raps the news” make sense? How about “Obama rocks the news?” Same principle.
It looks like the GOP is trying to present Mitt as serious and formal while Obama is singing songs and playing around. That will probably play with some people, but to me it looks a little bit like sour grapes that their candidate isn’t someone who would pull a big audience on a talk show or news comedy bit. Obama is the POTUS, so he has gravitas coming out of his ears already, plus he can communicate in all these modes to which the GOP appears to be deaf. Which guy looks more able to put on a game face to speak to the Colombian leader, or the Russian or French or whatever leader?
As Obama explained, “POTUS stands for President of the United States”. 
Which is probably part of why the Republicans have been trying to portray talking to other world leaders as a bad thing.