Conversely, the groups that spend a lot of time on poverty - the Center for Budget and Policy Priorities, or Families USA - aren't member-driven. They're advocacy organizations, they tend to rely on foundation grants or endowments, and they tend to play a bit more of an inside Washington game, because they don't have funding sources or a membership structure that lends itself to grass-roots pressure. Foundations, after all, give a lot of money for research, but not that much money for attack ads. And people living just above the poverty line don't tend to send in $100 when you tell them subsidies in a bill are about to be cut, even though those subsidies will hurt them a lot more than the public option will help most of MoveOn.org's members.
Put another way, the basic problem is that poor people, by virtue of being poor, can't donate a lot of money to popularize their concerns, and are fairly marginalized from the political process in general. The result isn't that those concerns are entirely ignored in Congress, as many of these institutions are very effective, and many legislators take this stuff very seriously. . .
The effects of this can be a bit weird: The health-care bill, for instance, spends pretty much all of its money on the poor, and its structure is primarily designed to increase coverage among low-income Americans. But pollsters have advised Democrats not to talk about that, and so they don't. Instead, they talk about how insurers are evil, or the public option is good, because those issues are more resonant both among the broader electorate and the liberal base.