Let’s make a few general statements first:
Jesus was not the government. Jesus was not a republican (nor a democrat). He did not live at a time when general wealth was as great, nor did government have nearly the capacity it does now. However, anyone who thinks Jesus did not advocate for the poor is simply wrong. To imagine some system in which Jesus wanted less government, and expected charity to take care of the poor is equally misguided. To give to Caesar what is Caesar’s is to have some faith that the government can do its job. Did Jesus expect people to work? Sure. So did Paul. They both also knew that not everyone can find work. Did Jesus think there would be a welfare state? Yes; he said “there will be poor always.” I am guessing that Jesus, were he alive today would advocate for a mix of government and private charity to help the poor, like we do have. And he would appreciate programs that give more than handouts, those that encourage people to invest themselves.
Under Eisenhower: High
Kennedy: headed down
Johnson: headed way down
Ford: wavering, headed down
Reagan: Went way up, then headed down
Bush: Headed up
Clinton: Way down
W Bush: Headed way up
Obama: still headed up
Now, let’s see the history. Do Republican presidents help reduce poverty? The evidence shows, generally, no. And do Democrats reduce poverty? More often, yes, but not necessarily. Does government welfare always work? Not necessarily. Is charity enough? History says, clearly not. But there is more to it. A rational assessment is that poverty goes down under two conditions: a healthy, innovative economy, and fair taxes. A healthy economy does not come about simply by leaving the rich to increase their lot. We cannot escape the role of government in affecting the economy (sometimes this is by war accompanied by innovations, sometimes by government investing in research and development, and sometimes by other global factors, but pure laissez faire is not associated with anything besides wealthy protecting their loot; not low poverty, not high employment). Neither an innovative economy nor fair taxes is going on right now, and poverty is way too high. Unemployment improves with the exact same conditions. Government can help with fair taxes and with assisting innovation.
I think all the other shouting matches are a waste of time.