Here's the relevant page for anyone to lazy too click through. He even goes on to say "perhaps I am wrong as to the exclusion of the presidency, no doubt I am."

There was also some interesting debate on if it should expire after 1870, and the response was a pretty resounding no, it should be the law of the land forever. Some people recently have also pointed out the phrase about giving congress the power to enact laws to these effect, suggesting it doesn't do anything unless congress makes a specific law enforcing it. That didn't seem to be the view when they added it in to the amendment though, they wanted to say congress explicitly had that power so that it could override state law if states were in conflict with the constitution here. There was a concern that if they didn't add that, then only states would have the power by definition (any powers not explicitly given to the federal government are devolved to the states), and confederate states might choose not to enforce all the provisions of the fourteenth amendment. This would let congress explicitly over ride state laws in respect to equal protection and other parts of the amendment including the insurrection part. Obligatory IANAL disclaimer, but it was very interesting to read through. Some of the things I'm referencing were from an earlier day, may 23rd, there were a number of days where the amendment was brought up.