I just talked to my local home brewer store, and was told that leaving beer in your primary fermenter after the gravity has stopped changing will actually PRODUCE off flavors instead of eliminating them.. the manual that came with my kit also recommended 5-7 days. Seems like everybody's dead-set on their opinions! We'll see how this turns out..
That is possible. Though in beer it isn't horribly likely. Occasionally the yeast will run out of some key nutrient during the cleanup phase and release an enzyme that breaks down dead yeast cells and releases the nutrients in them. That produces a lot of unwanted compounds in addition to the nutrients that are needed by the yeast. Most notably H2S, which smells pretty much like rotten eggs. Many people don't realize this can happen anytime you have live and dead yeast cells in the same solution, not just during the actual fermentation.
The thing is, I would be gobsmacked if this happened to somebody brewing a normal gravity beer. The wort of a typical beer is so loaded with nutrients that are inadvertently extracted along with the malt sugars that this is extremely unlikely.
To be frank, this is only a problem I've ever had with certain types of fruit based wines. Usually with ones that do not contain much in the way of yeast friendly nutrients, and have high abv targets.
IE: Peach, lime, blueberry, or strawberry. That's one reason why it's more common for wine to be racked to secondary.
If, on the off chance, you do get the problem you would want to move your beer to another container and leave the yeast cake behind. That way you won't have as much material to break down. If it happens after fermentation your probably to late to add nutrients and address it that way. Once your off the yeast cake, I would advise adding 1 old penny per gallon of beer to the brew.
That needs to be a 1981 penny or earlier, or it isn't copper and won't work. Though anything that is uncoated copper will work. Then stir/shake the living **** out of it. That will release most of the H2S from solution in the liquid. Small amounts of copper oxide will form on the outside of the penny and have a little party with the H2S. The result is a form of H2S that isn't water soluble and will settle out of solution fairly quickly.
If you get a rotten egg smell during primary, then you would want to add yeast nutrient, then rack to secondary and do the copper and shake thing. You would need the nutrient to keep the new yeast growing from doing the same thing as the old ones.
If you did leave in primary for more then 3 weeks you might get some breakdown of yeast cells without the need for the enzyme. It's more typical for that kind of thing to start 4-6 weeks after fermentation is complete though. At lower temps this can even take 2-3 months.
EDIT: I'll say it again in case I forgot. Chill. Beer isn't that hard to make. You might not have exactly what you wanted, but it will still be beer. Plus it will almost certainly be better then your typical macro brew.