The problem with primary transcripts is that they are processed and degraded, these portions not very likely to yield high coverage in sequencing. They might appear as a weak signal surrounding the mature miRNA. If you know a true miRNA location, one could look for weaker signals surrounding it. If the miRNA is transcribed from an intron, I see marginal chances for separating the signals at all from the background.
What Michael says is true, but you might have better luck if you design an experiment that gives you a better chance of finding what you're after.
For instance, as part of their work on the ENCODE project, Tom Gingeras' group has run RNA-seq on different sub-fractionations/sub-compartments across different cell lines. They have all different combinations of polyA+ and polyA-, long, and short RNA isolated from cytoplasm, nucleus, nucleolus, etc.
Perhaps you'll have better luck looking at RNA taken from within the nucleus to get what you are after. Unfortunately I can't link directly to the page for this project since their web-site is in (poorly written) flash, but just go to the lab's home page and click on the
Projects > ENCODE menu item.