The idea of implicating prayers says that we must be acting and doing in the world in ways that support and bring to life the words of our prayers. Some who advocate for such prayers also advocate for the government to continue to take the leading role in combating poverty. They don't see the two as being contradictory. Instead, they often see them as consistent with each other. In both cases, they argue, they are utilizing and leveraging the resources they have (personally and politically) to drive resources to the poor.
But that's only true if 1) the government's actions toward the poor were effective in helping the poor, 2) those actions were not significantly wasteful, and 3) doing so was not giving to Caesar what irrevocably belongs to God, and therefore to the Body of Christ, to address and accomplish. I don't think any of these three things is true.