The last thing you would do is send the President to a radio show to talk about a temporary resolution. VP’s have to have something to do and this is exactly it.
Not saying I agree with the rest of the story...that’s irrelevant to the question of who should go on the show.
Trump would be the best person to explain what he did and his strategy so his base is up to date. Not Pence who may or may not articulate the position well.