My view, which isn't worth much, but it's nice of you to ask...
1) Voters don't care about the Department of [whatever].
2) Voters care about getting their government-provided services. So if DOGE cuts result in slower processing of social security payments, or VA benefits, or some other money or thing that the government promised, voters will care a lot.
3) Rumor has it that those kinds of delays are already taking place and will occur a lot more frequently. If so, that will be a huge problem for Trump.
4) Voters care a great deal about their own jobs and the economy. If you are a voter in a place with a lot of federal workers, and you or people you know lose a job because of DOGE, that will be a problem for voters. If the area you work in goes through a bunch of economic trouble because the federal work force there sustained a significant part of the economy, that will be a big problem for you.
5) Voters also car a great deal about certainty. We don't want to live in uncertain times. So the more up in the air things feel, the more nervous people will be. Right now, what's happening feels uncertain, but just a couple of months into the new administration, that's ok. If voters feel this way in 6 more months, that will be a problem.
6) Yes, there will be $1500 hammers, but probably not that many. The truth is the government is probably better, internally, than a lot of private sector companies. Most of the fraud is probably people and companies taking advantage of the government, not the government buying $1500 hammers--like the food stamp fraud you pointed to (and people not paying taxes, taking advantage of pell grants, taking advantage of medicare/medicaid, etc.). There probably is some redundancy, but that's not really "fraud, waste, and abuse." And how much of that is found / eliminated is an interesting question.
7) Finally, most voters don't know if any of these things are connected--they just will know how they feel, and whether they are getting the services and live in an economy they are happy with. That's a big part of the problem with the fiscal responsibility issue: voters know how they feel, not how GDP, debts, and deficits interact.
From a different perspective, I think we are seeing and will see government departments hamstrung by DOGE, which will mean the government is less efficient in doing its job. There are some programs that will likely get broken, and in the short term that will hurt people that "we the people" think shouldn't be hurt. In the long run, it's very possible that this will lead to an opportunity to remake these departments/programs in a way that is an improvement. That long-term goal isn't a bad thing--the question is who gets hurt in the process. That's where the trouble is.
Finally, notwithstanding the mandate the voters gave Trump, we are still talking about pretty fine margins in the world of politics, so it doesn't take turning off that many people to result in a political change. Pretty good bet that such is coming. The question is where we will be when it arrives?
