Asymptotic growth?

This afternoon, the NPR program Marketplace included a story, “Campaign fundraising, pre- and post-primaries“.Host Kai Ryssdal interviewed American University history professor Allan Lichtman.  The following comment from Lichtman caught my ear:

The amount of money raised by presidential candidates has just asymptotically increased in recent years. It’s doubled and doubled and doubled again.

I’m one of those people that is amused by people who describe things as having grown exponentially when, in many cases, they have just grown slightly faster than linearly.  (I’m particularly amused when the market share of a product is said to grow exponentially.) But in this case, we have real exponential growth — it’s doubling periodically. But asymptotic? Did he really mean that the amount of money raised will be infinite at some point?

Perhaps he was just being hyperbolic.