I would probably use ‘une élection haletante’, from haleter (to pant or breathe heavily). It preserves the connotation of the election being suspenseful as well as the neutrality between the possible positive (thrilling, exciting) and negative (tense, concerning) connotations of ‘nail-biting’.

‘Une élection palpitante’ could potentially work, although it has more of a positive connotation, one which is less neutral than ‘nail biting’ and closer to ‘thrilling’ or ‘exciting’.

There is also the option of the more straightforward ‘une élection pleine de suspense’, which has quite a neutral connotation.

You can say:

Cette élection se joue sur le fil du rasoir. (on a knife-edge)

Wiktionnaire:

(Figuré) Se trouver dans une situation délicate dont l’issue est incertaine.
La situation se complique ; je suis vraiment sur le fil du rasoir.
Si les commandes ne rentrent pas, pour notre trésorerie, ce sera sur le fil du rasoir.

Definition from expressio.fr:

dans une situation instable ; dans une situation dangereuse ; dans une situation critique ; dans une situation susceptible de mal se terminer ; sur la corde raide ; sur la brèche ; au bord du gouffre ; à l’orée

I think the expression you are looking for is "Coude à coude" referring to a race where contestant are at the same distance (there elbows are next to each others)

By the way if you google it right now you will find articles about the US presidential election

An expression I hear from time to time is

Se ronger les ongles jusqu’au coude

This means to bite your nails up to the elbow. It is meant to be humoristic so certainly not appropriate for the US elections for Americans.

So it’s at least in part something "that causes people to feel nervous because the ending is not known until the final moment" (Merriam Learners) and therefore anxiogène, "which creates anxiety", is one option for a negative connotation i.e. une élection hautement anxiogène. Maybe if it’s construed a bit like a cliffhanger then (une élection) qui tient en haleine (jusqu’à la fin i.e. until the end) is another alternative since that means "tenir dans un état d’incertitude, mêlé d’espérance et de crainte" (Wiktionnary; i.e. to "hold in a state of uncertainty, mixed with hope and fear" something, my translation)… "Qui tient en haleine" is quite similar to something suggested in another ansnwer.