The most obvious answer, at least to me, is that, Alex probably feels that, compared to Quentin, who has just inherited an estate, they are broke. They do seem to be doing a lot better than Will and Carolyn Loomis, the closest to counterparts they have on the series. Alex claims that they're broke but at least they're not having to take in boarders, vampires or otherwise. And it's only Alex who makes that statement. Claire doesn't put up an argument. She just remains quiet. Claire may be making enough trips to Gregory's boutique to be recognized as a regular customer but, outside of that, what expenses do she and Alex actually have at Collinwood? Rent is apparently not one of them. Food seems to be minimal. From what I can see, Alex seems to be the more impulsive of the two.
And, while I'm thinking about it, why did he and Quentin hit it off so well when they first met? By his own definition, starving artist Quentin was mean and surly. Claire couldn't figure him out. So what made the two of them bond?
Or perhaps The Jenkins are simply bad with money. Or maybe they just had the same literary agent as Lara Parker.