We can forgive xkcd and assume that the "you" in the third panel is singular, not plural. Then it's just a budget constraint. But of course I'm not going to pass up an opportunity to point out my accounting identity pet peeves.
Y=C+S, so the uncritical mind comes along and says "if we increase consumption we can't save as much, therefore we can't invest as much". What the uncritical mind doesn't realize (and why it ends up completely bungling the paradox of thrift), is that Y=C+S is just a relationship that has to hold at any given point in time - it's not an explanation of what determines these variables. This could also be written as Y(other stuff) =C(other stuff)+S(other stuff). Depending on what's going on with the "other stuff," you could have an increase in the consumption rate and a increase in all three variables, or an increase in the savings rate and a decrease in all three variables. Or something completely different.
Anyway - I appreciate the strip a lot. One of the things I've always enjoyed is complaining about TV commercials - meaningless claims, obvious inconsistencies, etc. It used to bother Kate, but now she does it too. But take a critical eye to xkcd's third panel.