The thing about evolution is that it is the result of organisms with favourable mutations having an increased chance of surviving long enough to reproduce, and the next generation likewise and so on. The problem with mermaids (assuming that the term refers to both male and female individuals with a human-like body and head but a fish-like lower torso and tail) is that the upper and lower portions of the body are favourable mutations for completely different environments.
Let's look at the upper body first. There is a head which naturally orients to look in a plane perpendicular to the axis of the spine, with both eyes spaced apart but looking in the same direction to give good depth perception but poor all-around vision. The arms and hands are adequate for climbing in conjunction with legs, good for tool use, and combine with the eyes to make humans the best throwers of rocks and spears on the planet.
Now let's look at the lower half of the body. It's a fish-like tail. It can presumably propel the mermaid through the water fairly quickly, and it is completely useless for anything else.
Put the two together and you have a creature that is fairly bad at everything. In the water:
- the neck needs to bend at an awkward angle in order for the creature to see forwards when it is swimming
- the mouth and nose are badly positioned for breathing without breaking out of the water completely (there's a good reason that whales and dolphins have blowholes and other mammals have nostrils at the front of the head, not the underside)
- the body and head are unstreamlined, with arms that are poor at underwater swimming and cannot effectively throw objects underwater.
On land - well, it can flop about a bit, but the arms are unable to propel it effectively due to being too far forward of the centre of mass and the head is again at the wrong angle to see where it's going without straining. It's climbing-and-throwing optimised arms are pretty useless with a fluked tail down below. The only real advantage of the hands, arms and head arrangement is that the mermaids would have the tool-using ability to make seashell bikini tops, which only helps them survive predation by modern film censors.
Put another way - if the hominids need to spend more and more time in the water, eventually becoming almost fully aquatic then they are likely to eventually end up looking like dolphins or dugongs (the latter having been suggested as a possible source of mermaid myths). It is only if they stay on land that the upper body and head will look "human", but then they must have the legs to go with it.
As for timeframe - you are quite correct that 6 million years is not very long for such a radical change, it is about how long it took humans and chimpanzees to diverge from a common ancestor (5-10 million years). Changing from having two distinct legs to a fluked tail is pretty much what happened with the evolution of the Sirenians, which took close to 50 million years. In order to knock an order of magnitude off the required time there would need to be very strong environmental pressure (at just the right rate of change to be survivable by evolving) combined with an increased rate of mutation, whether as a result of radiation, chemical pollutants or viral action. Given that most mutations are disadvantageous, greatly increased reproductive rate and shortened generations would be necessary - which unfortunately means that the mermaids probably aren't the sharpest tools in the shed intellectually in addition to their other disadvantages.
In short - the timeframe is barely manageable by ramping up the environmental pressure and mutation rate, but unfortunately I cannot see any justification for the contradictory upper and lower body elements being a survivable evolutionary path.