It is sometimes argued that American politics is bad for the poor because (a) interest groups have a huge amount of influence through campaign donations, etc., (b) the poor are not a powerful interest group. One could attempt to solve this by taking steps to decrease the influence of interest groups; however, this is not feasible because everyone currently in power is beholden to a range of interest groups: in particular, incumbents gain enormously from interest-group connections, and would be less safe if the groups did not exist. Besides, the swing-voter subset of the public is too ill-informed and clueless to care about relatively high-order "process" issues like campaign-finance reform. In addition to such practicalities, I would argue that lobbyists are a bit of a red herring: the real problem is that the poor are not numerically a powerful political force, esp. when one accounts for age-related disparities in voting -- democracies are, by and large, perfectly happy to give minorities the shaft. Besides, one could argue that technocrats (the alternative, I suppose, to vested interests) are themselves an interest group in some ways; in particular, as a socio-economically homogeneous bunch, they are liable to underestimate the costs of policies when these costs fall on other groups, and to overestimate the costs that fall on themselves and their friends. Very few policies are good for everybody or bad for everybody; most have winners and losers; in these situations, educated elites are likely to adopt policies that shift the costs onto other demographic groups.
One should, therefore, be concerned with how to make an interest group out of the poor: or, more realistically, how to align the interests of the poor with those of extant interest groups. A naive approach to this is Tony Judt's "social democracy of fear" idea -- persuade the [lower half of the] middle class that, in an uncertain world, it is desirable to have some stays against extreme privation. Unfortunately this idea suffers from bad psychology: in an uncertain world, what people actually do is cling bitterly to whatever they have, and protest mosque-building. (However, it is possible to get the middle classes to support existing programs that they benefit from.) The next most obvious solution seems to me as follows: have the govt. subsidize groups such as health-insurance providers, transportation companies, etc. to provide services to the poor and perhaps to employ them. In order to pay for these services, one will need tax raises; if geared toward the super-rich, these might create conflicts of interest between corporations and their CEOs, so gear them toward the middle class or even the poor, by flattening the tax structure somewhat. In other words, if a policy redistributes wealth both upwards and downwards from the middle class, that would mean (a) an interest group with clout will defend the policy, (b) it will ostensibly serve the poor and thus might keep the socialist left only boundedly unhappy. Certain segments of the middle class will be extremely irritated but they would probably have voted Republican anyway.
This sort of coalition of the rich and the poor against the middle class has happened in the past; I believe it was the basic political alignment in 18th-century England. As the GOP's populist-nativist streak grows stronger and stronger, I suspect that this is the sort of anti-populist coalition that would have the best shot at keeping the GOP out of power. The most serious danger is, of course, that the corporations will pocket the money and not provide services to the poor; this can to some extent be ameliorated by making the services broad-based so that the middle class (which is vocal) gets to benefit from them. (They wouldn't be getting their money's worth but I'm not sure they'd notice.) So -- in short -- we should be soaking the middle class in order to provide broad-based services that would make help the top 2% and the bottom quartile. The (electorally necessary) remaining 23% can be picked up through social liberalism, cosmopolitanism, and other "values" issues, as well as by buying the votes of clueless independents w/ the money of the top 2%.