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I am not aware of any empirical data that shows a causal link between poverty and terrorism. If there was such a link then we would see poor people and communities more involved in committing/planning terrorist attacks than the current data shows. Poverty by itself simply does not have the direct radicalizing effect on individuals.
In fact, the majority of empirical studies on terrorism provides little indication of correlations between socioeconomic factors such as poverty, inequality, and unemployment and the incidence of terrorism. For example, the data in Alan Kruger and David Latin's global study of the origins and targets of terrorism lend little support to the notion that poverty leads to terrorism, instead suggesting that limited political rights and civil liberties tend to be the most influential in inciting people to terrorism and country-level economic factors such as poverty and high unemployment, tend to be most relevant in determining the targets of terrorism [see here (pdf)]
As analysis of the home-grown terrorist problem in Europe reveal, the reasons that may push certain second and third generation Muslim youth toward violence are generally not specific enough and include traits shared by a larger population that deals with similar situations in very different ways. In fact, as Matthew alludes to, the process of radicalization is a complex interaction of factors, external (such as poverty, perceived humiliation, radical ideology, and American foreign policy), social (e.g., social identification mechanisms or social network dynamics) and individual (e.g., psychological characteristics or personal experiences), which do not necessarily lead to violence and not every radical becomes a terrorist.
The challenge for the US and other government and non-government stakeholders is to better understand the mix of factors that are relevant to the particular country/region and develop policies and work with the right mix of government and non-government actors to try to address these factors. Given the heightened sensitivities surrounding any program aimed at countering the radicalization process that has the "Made in America" label on it, however, it is important for the US to work with (or under the cover of) partners, such as the UN, whenever possible (and certainly more than it currently does) in developing and implementing programs in the wide range of necessary fields (e.g., social/economic/political).