As a Brit, I do not know this character so there will be jokes I miss. There are a couple of very funny bits, I loved the Taylor Swift ticket line and the marshall arts angle was good. It is a good framework, but it is also rife for expanding the humor:
One important moment that even he called the best of his career is arranging the government shutdown of 1995. But over his two decades in the House, no one actually who this Kasich guy is. In fact, his colleagues nickname him "That Guy".
With a twist of irony:
Kasich's highest Political achievement to date was supporting the partial shutdown of the Federal Government in 1995, over spending money on education, health and the environment. With such a high-profile standing, and clear vision of a country full of uneducated, unhealthy, chemical burning squirrel killers, it was a wonder that after his two decades in the House, no one actually knew who he was. In fact, his colleagues nicknamed him "Erm... that guy... I think".
Keeping it simple, the strategy is a wry bio of a US Presidential Candidate. It needs some daft transitions and unpredictability, like the Taylor Swift line. Bring it back to earth occasionally and keep the reader off guard with a finish they won't expect.
The article's overall quality - that indefinable something.
Nice piece that covers a US Presidential candidate, it left me wanting more. There is a lot of humour to be drawn out of those paragraphs, expanding on the detail of events with a view to injecting jokes and lines. This would beef-up the article without having to add more information.
I think that it's an OK article, but it's slightly lacking, though it has potential. There are some bits that I like, such as the milkman reference, the Taylor Swift joke, the kung-fu and the 'crazy' Ted Cruz remark†. However, I think that the 2016 election section could be expanded upon. The ending is also quite abrupt - I don't think it should talk events in the future (such as the Ohio primaries), and it's a bit too truthful where it could be perhaps more biting (i.e 'However, he was considered the sane one in the debates and that led to abysmal polling for him.'). Remember that Kasich did quite well in Noo Hampshire, and he's one of the 5/22s of the Republican field who hasn't quit yet, so perhaps there's more to come that you can add.
As one who hails from the UK, I can't give you that much input on Mr. Kasich as I don't really know the man. But I still think that this article has potential, and I hope that I've been able to help you in any way. :)
†I like the idea that there's a 'crazy wing' of the Republican Party. Would it be possible to expand on that, possibly linking to another article or something? Or would the whole joke work better in a different article?