Nomination comes first
When election season arrives you pick a seat and face your party's Nomination Review. The candidacy card shows two separate bars, your nomination odds and your general-election odds, plus the combined figure. If the first bar is low, a strong general-election position is worth nothing.
The review weighs Party Trust, Approval and Fame. Holding the seat already helps a lot, and being in the party's main faction or having a living mentor adds a little more. Unexplained flaws on your record pull the odds down. When you are cut, the game tells you in one line which factor hurt most.
If you lead a party you founded, you skip the review and become the candidate outright. Growing that party is then your job.
The presidency is a Primary
Presidential candidates are chosen in a party Primary rather than a review. Your rivals are the party's heavyweights, so Party Trust, nationwide Fame and your overall ability matter more than Approval. A spell as party leader, a cabinet post or a Governor's office all count in your favor.
The fork after the cut
If the party picks someone else, three roads open up. Accept the result and your Party Trust rises while you wait for the next election. Leave the party and run as an Independent and you are on the ballot at once, but you carry the "party hopper" label and the general election gets harder. If the conditions are right, you can found a party and run as its candidate.
There is no fixed right answer. Some lives accept every cut and end as a political drifter. Others flip the seat as an Independent, build a party and reach the presidency.