This is a strawman argument. It is of course mathematically possible to obtain a billion dollars (although notably much harder to do in a way that is liquid, but let's gloss over that). My somewhat more charitable reading of that claim (shared by other readers here, I see) is that ‘earn’ refers to moral desert. I'm not really a desert-oriented person but let me try to steelman it a bit:

In aristocracies we traditionally assume or imply that a person can deserve a certain wealth or power simply by being born into it. Capitalism, however, sells us the dream of the meritocracy: your (financial) success in life should depend not at all on factors of chance like birth or genetics but simply how much of yourself you choose to sell to the market.

At any point in time you have control of some tangible or intangible capital, including wealth, physical health, social connections, equipment, information, trained skills, et cetera. Some of these assets are gained by luck, e.g. accident of birth; some of them are gained by trading your time; and some of them are gained by spending another asset (whose origin reduces, recursively, to some combination of luck or time). At any point you can, assuming the market is appropriately liquid, spend some of these assets to get cash.

Some of these assets have force-multiplier effects on your future output in certain domains, from which exponentials naturally arise; but the time spent on them remains linear, and so, if we want to ignore inherited factors (the opportunity to spend the time on things without immediate feedback, say, or handed-down insight about which of these investments will produce the most value in the future, or access to the required tutors) the increase in earnings these things _merit_ has to remain linear as well. There is no way to compound your time and therefore, under an assumption of meritocracy, there is also no morally acceptable way to compound earnings, which I would assume is the point the politician is attempting to make. Under this worldview, any exponential compounding that occurs must, mathematically, be a result of systematically undervaluing the time of an exponential number of other people, since each person can only spend a linear amount of time.

In practice, of course, the assumption of meritocracy is simply wrong, and arguably the concept as a whole is internally incoherent (or at least I don't believe we've yet managed to articulate it coherently: we would have to settle the nature vs nurture debate and completely sever the value of a person's spent time from the accidents of their birth, if such a thing is even meaningful). But I think that's where the claim falls down, not in failing to understand the mathematics of exponentials.