Sarcasm aside, the point about the minimum wage is telling: No increase in the minimum wage occurred since 1997 until such time as Democrats were the majority party in both houses. The period 1997-2007 was the longest period in the entire history of the minimum wage for which there was no increase. (The second longest period was in the 1981-1990, during the Reagan-Bush years.)
The 2007 increase was introduced in Congress by George Miller, D-CA: All 233 House Democrats voted aye, while the Republican vote was 82-116 against raising the minimum wage, even after ten years. In the Senate, the Republican vote was 5-43 against, and since only 40 votes are necessary to prevent cloture, the increase was defeated until some compromise riders were added to the bill.
The last increase, passed in 1996, was not as controversial: this time, only 34 members of Congress voted against it: but all of them were Republicans.
The last increase before that passed in 1989: 45 members of Congress voted against it: 43 Republicans and two Democrats. (Incidentally: one of those two was George Miller, sponsor of the 2007 increase!)
So, while you're trying to snark at a claim that one party cares more for the poor than the other, I'm providing evidence that backs up Mensch's point.