Well, if they have experience with mental illness in any form (loved ones, they have it themselves, etc), then its not too bad, though it is always frightening and saddening to some degree to hear these heartbreaking words from the mouth of someone you care for enough to dedicate yourself to. If they dont have any reference for these things, then I think it is not only hard for them to understand but it scary. So is anything new really, but this subject is sensitive as death is very permanent and humans have evolved to have that SI to be insurmountable (most of the time).
From personal experience, Ive dated both people who have no experience with depression or anxiety, and then some who very much did (even more than my severely depressed butt), yet all of them considered me to have too much baggage in the end. So if you do mention it, then perhaps dont dwell on it. Dont delve into details (unless they insist on knowing), and if its really bad, perhaps tell them in broad terms (e.g "My depression is really bad lately and I have thoughts of hurting myself that wont go away" versus "I keep picturing myself slitting my throat"). Maybe even tell them to let you know in case you ever unknowingly talk about it too much.
In a perfect world, your partner would be someone who, if they cannot understand what youre going through, would at least sympathize and be compassionate.
This is all just my two cents.