I don't know whether welfare is the right term or not. I don't know who they are, so I don't know if they need larger subsidy checks or not. That's another discussion and not relevant to my point.
Here's my point...
A tax cut reduces the level of tax one pays. If one does not pay taxes, then one cannot receive a tax cut. Instead of calling your plan a, "tax cut plan," our useless politicians could say, "we have a plan that will reduce taxes for some and will provide larger subsidies for others." It's longer and has more syllables but it does have the benefit of being the truth.
I know why our delightful politicians don't do this. They're liars by nature. They call the entire plan a tax cut leaving out portions of the truth because it will look better in a headline in the New York Times or someone's RSS feed. Things change. They also remain the same.
If you are waiting for a new era in politics, you have been given ample warning that you aren't going to get one.