There’s an old saying, “cutting off the nose to spite the face.” It refers to doing something for revenge or spitefulness that is really self-destructive. This describes the Right’s attitudes toward health care reform. Apparently it's more important to punish illegal aliens than to provide health care for ourselves.Actually, I'd say it describes a common conservative attitude towards almost anything to do with the government helping people. All recipients of governmental aid can be divided (theoretically, at least, and probably crudely as well) into two groups; those that "deserve" that aid, and those that do not (the specific metric by which one is judged to deserve aid is a topic for another time). Almost by definition, a conservative will tend to believe that the most important thing to do is to minimise the latter group. Liberals, I would argue, tend to focus on ensuring the former group is maximised.
Of course, not only is the liberal approach more empathic (a word I haven't used in a little while, so I feel OK deploying it again), but it has the benefit of not being impossible to achieve. The conservative approach may move the line regarding what qualifies as "deserving", but it is fundamentally obvious that doing so will not decrease the number of people getting something they don't deserve using the new metric, because any line you draw will always lead to people just short of the line claiming to have crossed it . You either accept that, or you give away nothing (which may or may not be something the conservatives in question want, though none of those that I've spoken to have ever admitted to that).
As far as I can see, allowing people who (arguably) shouldn't have X to receive it is simply a cost to be factored in to the process of doing what we're supposed to as a society, which is giving X to those in need of it. You can argue that people don't deserve something, but it seems a fairly weaksauce argument to claim that people who do deserve something shouldn't get it to make sure that those who don't deserve it can't have it either. Contra maha, it isn't a cut-nose-spite-face type of deal, since those doing the cutting know full well they still get to be able to breathe and smell the roses, but that makes the attitude all the worse.
 I grant that whilst the number of cheats may not go down, one could ensure the total cost could. Interestingly, though, conservative discussion of the issue often focuses on the people doing the cheating, rather than the specific amounts involved. I admit that that's not always the case, though. Besides, either an amount of money being lost is big enough that I'd be in favour of stronger measures to police the current line (rather than moving it, and wherever possible that the policing be done ex post facto, i.e. we catch cheats after they've cheated, rather than holding up potentially truthful applications interminably), or it isn't, in which case I would suggest it's not worth getting worked up about in any case.