Prepositions – How to Choose the Right Preposition After “Negotiate”

While you could use both "a" and "the" in your examples, it's much more common to use "of" in the indefinite case.

When using a:
You're talking about no particular item, but one among a bunch of others. the "of"-part serves as reducing the size of that bunch.

a habit - well, there are many habits out there
a habit of mine - one of the few habits I have

the love - now, that term is mighty unspecific, isn't it?
the love of a good woman - oh, that kind of love, I see.

When using the:
You're already talking about a very distinct subset (namely one occurrence) and other ways of showing that are available.

the habit of mine - my habit / that habit (i was talking about)
the love of the good woman - that good woman's love / her love

Consider these possibilities:

I am stuck on the database problem.

This means you can't continue because you can't figure out how to solve the database problem.

You could also say

I am stuck at the database problem.

This means much the same thing, with the nuance that you are stuck at the point of the database problem among a set of tasks you are trying to address serially. You probably can't do anything else till you solve that one. If you use on it might suggest you could do other parts of the task while waiting for enlightenment on the database issue. But on and at are pretty much interchangeable here. I would expect to hear on more frequently.

I got stuck with the database problem.

This means someone left you or assigned you the database problem to solve (with overtones of it being an unpleasant or difficult task).