The fact is that we are once again, as in the days of the early republic and not in the heyday of the Progressives and the New Dealers, a republic of property owners. Most Americans have accumulated — or will, during the course of their working years, accumulate — significant amounts of wealth. And that is why, I believe, American voters seem to be rejecting the policies of the Obama Democrats.
Reinhardt's point, made using the research mentioned above, is that most people in the U.S. own very little property, since almost 50% of families have net worth (including homes) of $10,000 or less. So Barone is just wrong to claim that most Americans have or will accumulate "significant" amounts of wealth. Of course, if you believe that significant in this context should mean more than zero, I can't help you.
I think that Barone is onto something, though, as is so frequently the case, not what he intended. The definition of republic is:
a state in which the supreme power rests in the body of citizens entitled to vote and is exercised by representatives chosen directly or indirectly by them.
Barone was talking about a republic in the Jeffersonian sense, apparently, a republic of small property owners (or for Jefferson, yeoman farmers). What we have, essentially is a republic more in the Roman mold, where the property owners are the citizens entitled to vote. But, you say, there are no property restrictions on voting in the U.S.! Right you are, but there are certainly property restrictions on who you get to choose from when you go to vote. More accurately there are property restrictions on who gets to decide who you get to choose from. In this unintended sense, Barone is right. Reinhardt is also right to say that we are not a nation of property owners.
We are not a nation, but a republic of property owners.