With meditation, you can't push. Meditation is one of those things that cannot be forced. You just have ot make yourself available, and we do that by being still, being at ease, and paying attention. The depth you are looking for comes from letting go, not from "pushing deeper." But in any case, you shouldn't be so concerned with how deep your experience is. Consciousness is infinite. You could have a more powerful, more profound experience of it, but it is still the same infinite ground that you are speaking about. That is why, when we try to describe the experience of consciousness, words always fall short. We might use words like "powerful", "profound", or "deep," but the words are only a metaphor, a quantification of infinity, for that which cannot be measured. A little bit of infinity or a lot of infinity -- it's the same thing.
So you shouldn't worry about how meditation is supposed to feel, or spend too much time comparing your experience to what you may have heard from others or even to what you may have experienced yourself in the past. You are entering into a realm where measurement doesn't mean anything. Dwelling upon too many ideas about what meditation is supposed to be like is just a distraction from your own direct experience. Just make yourself completely available and then see what happens. The state of meditation is an immediate one. It doesn't require time. But if you're holding on to an idea of a particular kind of experience that you are convinced you need to have, you are not going to be able to see deeply into the experience that you are having right now.
Meditation -- and indeed, the recognition of enlightenment itself -- doesn't have anything to do with any kind of experience that you can imagine with the mind. The state of meditation, which is synonymous with enlightenment, is the freedom from experience, and that freedom is always imminent. But it does require a ceaseless willingness to relinquish any ideas you have about how it is supposed to feel. Then you will discover the englightened mind. It's right here. It is always already the ground of your experience in each and every moment.
--Andrew Cohen, in "Being and Becoming"