But the Bible does not tell us to give it to the government in hopes of it getting to the poor, does it? And I certainly do not consider the government or politicians among the poor no matter how much they beg for more.
The truth is that giving to the poor goes hand in hand with the Gospel, not the government; see, e.g., Galatians 2:9-10, but there are other passages.
And when James, Cephas, and John, who seemed to be pillars, perceived the grace that was given unto me, they gave to me and Barnabas the right hands of fellowship; that we should go unto the heathen, and they unto the circumcision. Only they would that we should remember the poor; the same which I also was forward to do.