What this means is that whatever the level of damage across-the-board would impose, we can expect the affected agencies will try to make the damage look as high as possible.
Now, there’s a natural balance to that; there are plenty of things that the government does that are extremely important but are barely visible; no one would notice if no one inspected meat for a week, unless something went wrong. Of course, part of the strategy also involves publicizing as much as possible anything that does go wrong, and blaming it on the sequester (whether, in fact, it really is a consequence of the sequester or not).
Politicians involved need to be aware of all of this, going in. There’s some evidence that some Republicans, however, aren’t fully aware of the situation; I’ve seen references to the small percentage of overall spending that will be cut if the sequester goes into effect on March 1. As Collender correctly notes, all too many Republicans entered the 1995-1996 shutdown showdown with a mistaken belief that polling showing public antipathy to “government spending” would be the best predictor of reaction to a shutdown. Instead, the better predictor was polling showing that the public loves most individual government programs — or perhaps the better predictor was just that those programs are important parts of everyday life for everyone, whatever their politics. Democrats, too, should be aware that defense cuts that may poll well might also produce real, and very visible, pain.
None of which means that Republicans (or Democrats) should necessarily cave. But politicians on both sides should go into this with eyes wide open. Spending cuts are unpopular and this round will be no different. At least, not if the agencies affected have anything to say about it. And they will.