Resolving the problems of poverty are extremely difficult and may take generations to accomplish. Perhaps the Republicans aren't interested in even participating in resolving the problems and it is only the Democrats that have made any effort at all. I do not consider myself a Democrat or Republican, my voting decisions are based on who I believe is best able to do the job.
By the way, I don't think that a politician can eliminate poverty. Perhaps the best person for the job is a teacher. A politician only gets to decide how to spend our tax dollars. A teacher educates. Giving someone money (welfare) doesn't solve poverty, it just makes it worse. Educating people so that they can earn a living is the way to eliminate poverty.