While we think of "rich" as a quantity, I think in the parable "rich" refers to a state of mind.
In the parable (the parable of the "rich young ruler") it is the "love of money" which is the fundamental issue, not the quantity of it.
Some people are able to attract large quantities of money, yet are able to flow that money to others well. Others have much less, but their love of money leads to exploitation, hoarding, jealousy, covetousness, selfishness and so on.
The "love of money" is in many ways the antithesis of Christian theology. Which is why the parable explains how it's a fundamental stumbling block - what we'd call a deal-breaker.
American Christians are unfortunate to live in a secular culture which values money over everything else, and this has permeated into the church culture. One need look no further than the political support, by professing Christians, to a "rich man" rather than to a "Godly man" within their own party.
The "love of money" is the root of all evil, not the money itself.