I don't feel that he has guaranteed that all readers of the article will come to the conclusion you have reached. Here is how I could interpret his brief quote:

1. more in absolute terms (which they already pay due to higher income) 2. more in relative terms (progressive taxes) 3. more than now (what you claim).

I don't that it's clear what he means in in the story, though. It could easily be taken to mean "yes, we pay more, and we should pay more (than others) so I don't support the republican plan!". Your interpretation is also valid - "the rich should pay more (than we do now)".