Paul Golin of the Jewish Outreach Institute addresses the problem of financial need among some unaffiliated American Jews in an article for e-Jewish philanthropy:

At any given time, the majority of US Jewish households are not affiliated with Jewish institutions like synagogues or JCCs. There are many reasons why, perhaps the most important being that the organized community hasn’t made a strong enough case for the meaning and value of being affiliated. There’s a subset of the unaffiliated, however, who already understand the meaning and value – or who, like most affiliated households, simply want or need the services provided – but do not affiliate because of their own personal financial situations. And the size of this subset has likely grown during the recent Great Recession.

The problem, writes Golin, is not that Jewish organizations are unwilling to make accomodation. "[T]here is almost universal agreement among Jewish communal professionals that their organizations will make accommodations," he explains. "However, how that actually works is in no way uniform and in fact represents a serious barrier to participation. In most organizations, those accommodations are not advertised in any way – the impetus is on the financially-challenged to ask for assistance."

 Rabbi Mordechai Liebling made a similar point in 2005 in an article called "Money in Synagogues":

Many congregations state that dues payments should not be a barrier to membership, and reduced rates are available. But studies show that the process of applying for a dues reduction is humiliating. In some congregations the process itself is unfriendly — even to the point of asking for income tax forms.

(A digression: it's comical to me that we need studies in order to tell us that asking for a dues reduction is humiliating.) Rabbi Liebling also points out, however, that the outright payment of dues is not the only way in which socioeconomic status can become a barrier:

How obligated is the institution to help members feel comfortable? Little can be done about the cars members drive, the schools children attend, or the vacations families enjoy. But a great deal can be done about the assumptions that the synagogue makes. The synagogue needs to be very conscious of the underlying economic assumptions made vis-à-vis programs and public statements. Presuming that everyone is at least “middle class” and won’t have trouble spending the extra $10 or $20 for a special program or school event is incorrect.

Celebrations are perhaps the most visible manifestation of wealth differences. Synagogues can set standards or guidelines about the lavishness of a kiddush or even a bar or a bat mitzvah party... Hundreds of years ago medieval Jewry created sumptuary laws to regulate conspicuous consumption; perhaps we need to reconsider them.

To learn more about poverty in the American Jewish community, start with "Economic Vulnerability in the American Jewish Community", a report based on the the National Jewish Population Survey 2000-1. In 2008, the AJC published "The Costs of Jewish Living: Revisiting Jewish Involvement and Barriers". The BJPA also has many more holdings under the topic of Socioeconomic Status.