Trump’s first point of defense is that Section 3 of the 14th Amendment does not apply to him because it does not specifically mention the office of President or Vice President in the section about taking a prior oath to support the Constitution. While this argument likely will not be officially sanctioned by SCOTUS, it is worth noting that Gorsuch did ask questions along these lines.
Looking at the text:
Section 3 Disqualification from Holding Office
No person shall be a Senator or Representative in Congress, or elector of President and Vice-President, or hold any office, civil or military, under the United States, or under any State, who, having previously taken an oath, as a member of Congress, or as an officer of the United States, or as a member of any State legislature, or as an executive or judicial officer of any State, to support the Constitution of the United States, shall have engaged in insurrection or rebellion against the same, or given aid or comfort to the enemies thereof. But Congress may by a vote of two-thirds of each House, remove such disability.
it should be self-evident that the Presidency is an Office and anyone who holds that office is an Officer. It is the “Officer” designation in the second part that is being questioned. Again, it should be self-evident, that if the Presidency is an office of the United States, then the person holding that office is an officer.
However, to please the orginalists on the court, we don’t have to speculate what the framers of Article 3 of the 14th Amendment thought. It is documented in the transcripts of the Congressional Globe, a forerunner to the Congressional Record.
Maryland Democratic Sen. Reverdy Johnson asked: "Why did you omit to exclude them?" (referring to the President and Vice President). Maine’s Senator Lot Morrill replied: "Let me call the Senator's attention to the words 'or hold any office, civil or military, under the United States." Johnson conceded that this was sufficient.
The reason they specifically mentioned Senators and Representatives is because individual Senate and House positions are NOT considered officers of the United States and so are not included in the wording that covers the President and Vice President.
For an excellent overview of this topic see:
What the framers said about the 14th Amendment's disqualification clause: Analysis
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A second concern that kept coming up is this idea that we can’t have states where a candidate (Trump in this case) is on the ballot for a federal election but is not on the ballot in other states.
This too is a somewhat specious argument. We have had many elections where presidential candidates have been on the ballot in some, but not all the states. While all the candidates that fall into this category have been minority party candidates, there is no wording anywhere in the Constitution that says all states must have the same candidates on their presidential ballot, or that major parties should have “privileges” that the minority parties do not.
If SCOTUS accepts the argument that Trump can’t be disqualified by Colorado because he is on the ballot in other states, then what about candidates for minority parties that qualify for the ballot in some, but not all, states. Would this ruling mean that if you qualify for the presidential ballot in one state, then all the other states have to put you on their ballot too?
This problem can’t even be overcome equitably by making a national standard for ballot access given that all states have signature requirements to qualify. Clearly, given the disparate population sizes among states this could not be a hard number. But even if it was set as a percentage of the population of registered voters there is a second problem. What happens when a candidate meets the signature requirement in one or more states but not all. Do the states where the candidate did not meet the standard requirement now have to put them on their ballot?
The significant issue that was raised by SCOTUS is the potential politicization of Article 3 if they say Colorado can exclude Trump. I believe one of the legitimate scenarios given was basically (but not in these words): wouldn’t this allow the red states to gin up a reason to exclude the Democratic candidate and the blue states to do the same for the Republican candidate leaving only a few states to determine who the President will be for the whole country?
Well yes, but isn’t this exactly what is happening now? Isn’t this why candidates are focusing on those few critical swing states rather than the whole country? The only way to solve that problem is to get rid of the Electoral College and have the President elected by direct vote of the whole country.