Do I have to quit my job?

[Ronin]

I'm sure that getting fired is worse then resigning.

How so?

The thing that counts is, if you are an actual asset or not.
If you are working things out would probably require some initiative from your side, otherwise, they will let you go, regardless.

Walking out on your own judgement, before it's completely clear that you can't find an arrangement is just picturing you as a quitter.

If you don't want to get out of the job, don't quit, simple as that.

You can start to scout your options regardless.