I finally got around to watching The West Wing. There's a lighthearted small subplot of exactly this in S01E19.

By the way, it is so refreshing nowadays to watch a show about extremely competent imperfect people that legitimately strive to do as much good as they can, as they see it. Likewise with Sorkin's writing, while unrealistically witty and fast, it is a delight watching someone so obviously talented give their all to their work. Granted, as in other Sorkin writing, it does sound a bit like all the characters are just versions of him with different voices. But it seems to me like an intentional stylistic choice, a somewhat heightened reality.