Niehther party is anti-poor. Both parties have different ideas of what helps the poor.
Republicans belive the best way to help the poor is to improve the economy as a whole, creating more opportunities to lift them up out of poverty through work or investment and creating a higher average standard of living. Of course, in this model some don't or can't take the opportunities. Also, you have to work your way up (i.e. there's a few years doing minimum wage crap work, after you've shown you're a reliable employee you get a slightly better job at an office, ect.) This model expects people to grow.
Democrats belive they help the poor by handing out favors (welfare and artificially inflated starting wages, that you're not expected to grow out of) this model may lift the very bottom up a little, but drags the average down. It also doesn't expect people to grow, but expects them to stagnate.