"The election of a Republican would make the problem go away till the next time a Democrat was elected."
Is it unclear? It means the debt limit is a problem when a Democrat is president. And the debt limit is not a problem when a Republican is president. Or as you put it: "The implication was that it wasn't controversial until a Democrat became president." Or as Bowser put it: "The truth is it doesn't bother you until a Democrat is president."
If there's another way of saying it, then I leave it up to you to discover.