Chaim, welcome to Mi Yodeya.
I am not overly familiar with the changing nuances of "yeshivish", so I can't say that this particular phrase is something that I have heard verbatim. But, in addressing the concept implied by your question, you may want to gain some clarity between two similar terms - bitachon and emunah.
There are numerous articles on this topic, but I think this summary from "The Shmuz" is good:
The Rambam defines emunah as the knowledge that HASHEM created and
continues to run all of Creation. Simply put, nothing can exist and no
activity can occur without HASHEM.
Bitachon, however, is a quite different. The Chovos Halevovos defines
bitachon as trusting in HASHEM. It is a sense of relying on HASHEM to
watch over and protect me, as if to say, “I take my heavy burden and
place it on HASHEM.” While I am responsible to be proactive, I am not
in charge of the outcome, and I am not the determinant of the results.
I rely on HASHEM to care for me.
Emunah is a state of understanding; bitachon is a state of trust.
Emunah means knowing that HASHEM is involved in every activity on the
planet; bitachon means trusting in HASHEM in every situation.
A person can have emunah and not bitachon
So, to clarify the expression that you've probably heard, you are correct in that either you have emunah or not. This is kind of an absolute degree of understanding and appreciation. Either you believe that God is responsible for everything that happens or not. You can't just believe that God is responsible for some things and not for others. The concept of emunah is that God is involved in everything. If you don't believe that, you have a lack of emunah. I think a heretic involved specific stronger action then just a lack of emunah. I.e. this doesn't deny that there is a God, and it doesn't mean that you convince others of the idea. It's that you think that some things, perhaps, happen by God, but not other things. A heretic denies that God is involved in anything at all.
Now bitachon - yes, there are definitely levels to this. We see this every day in numerous people. Many people believe that if they invest in Amazon stocks today, that almost guarantees that they will make a profit in a year. What happens when that fails? They mope, they suffer distress, etc. They didn't trust that the ultimate outcome is up to God. They lacked bitachon. Or, opposite, I'm sure you've seen shidduchim break off because someone found a minor flaw in the other and thought that was major to not make the marriage work. If they had a greater level of bitachon, and trusted that God decides the outcome, they might have continued the shidduch.
In summary, I think people really mean to say "My level of bitachon is not great; I need to work on that." It is, possible that they were referring to "emunah", but, as I explained, above, it seems that emunah doesn't have degrees or partiality.