The parent of your post is a good example of how effective it is at doing that, especially when combined with the claim of an apparent wasteful use of that money. If you pay tens of thousands of dollars in taxes and hear about a million dollars of "taxpayer money" being supposedly wasted, your emotional response reflects an imagined scenario where all of your taxes went into that alleged waste even if individual income taxes alone represent over $2 trillion (i.e. million million, or thousand billion) of the US federal budget and your actual relative lifetime contribution to that individual project can't even be measured in cents.
Not to mention that the news sources referring to that spending as waste may be reporting on inaccurate or incomplete information (even when deferring to an official source) and may be misrepresenting or omitting the actual economic efficiency of that spending (e.g. the entire "condoms to Hamas" incident where the official announcement turned out to not only apparently have mistaken about US medical aid in Gaza specifically but also misrepresent the total spending on contraceptives for AIDS relief by the US across the globe as going to a single place - the benefit to Americans of providing contraceptives to HIV hotspots should be obvious enough).