Don't you think the people who are more zero sum, are the ones who are very focused on inequality (rich getting richer means poor getting poorer), who are also the ones who are most likely to support stuff like this? Direct payments, minimum wage, guaranteed income, welfare, etc?
We're talking about the poor here, not the middle class. A lot of states haven't raised their minimum wage above the federal minimum wage, which hasn't been raised since 2009.
Also even if wages go up inflation still reduces the wealth owned by the middle class. Especially given that interest rates on savings hasn't kept pace with inflation for decades. So unless you own a house or a stock portfolio even the middle class gets poorer due to inflation.
Sure that's an if, but the effects of inflation certainly exacerbates that inequality. Thus the rich get richer while the poor get poorer. It's just a question of cause and effect.
To add on what the other person said, the rich getting rich can indeed directly lead to the poor getting poorer. Money is influence, and especially in the US, a sufficient amount of money can buy anything. As the ultra-rich category of people accumulate more wealth, together they become the most important bloc to serve. Hell, you guys just directly cut taxes from the rich and raised on the poorest - what's that but not 'poor getting poorer'?