Poor people aren't actually that electorally powerful. Minority of the population and they are much less likely to vote or otherwise be involved in politics.
The issue is that the GOP as an institution is almost solely committed to policy that has the effect of upward redistribution. Note how Trump's only major legislation was another big tax cut for the rich and he proposed but barely failed huge cuts in gov't provided healthcare, and going forward, he's proposing more tax cuts for the rich along with a tax increase on the middle class. They get popular support for that agenda by stirring up cultural resentments, and they try to argue that policy that has a first-order effect of upward redistribution leads to higher growth. But the record does not support that claim (to say the least!).