For Tanks, the pop is instantaneous. For healers, the pop is quick (usually only as long as it takes for a single tank to q). For DPS, it can take a while. Just has to do with representative population. Best way to get these is to level as a tank or healer.
In my experience, levelling as a tank or healer is slow. I'm levelling a JG in tank spec at the moment, and planetside questing is significantly slower than with a DPS. I know a lot of people level their characters as DPS for this reason and and re-spec at 50. That probably means there's an even bigger shortage of tanks and healers at mid-levels than at end game. (At low levels it doesn't matter, because up until about lv20 a DPS is pretty much the same as a healer or tank, they haven't accrued enough skill points yet for there to be a huge difference.)