There are several Talmudic discussions about situations in which it is questionable whether it is necessary to get rid of chametz that is not readily accessible. The gemara[1] cites a baraita that when there is a hole in between the properties of two Jews, each one must put his hand in as far as it reaches in search of chametz. Whatever might remain beyond that point can stay, and it suffices to do bitul[2] on it. Similarly, a mishna[3] states that one does not have to worry about possible chametz underneath rubble. Again, the gemara[4] adds that one should do bitul. If it is known that chametz exists there, he must take steps necessary to remove it unless there are three tefachim (approximately 9 inches) of rubble on top of it.[5]
Perhaps the most pertinent gemara for the present discussion is the series of questions about chametz in out-of-the-way places in Pesachim 10b. The gemara presents two possible positions regarding the necessity to remove chametz that is on top of rafters. On the one hand, perhaps it is necessary to remove it, lest the chametz fall on Pesach and someone winds up eating it. On the other hand, perhaps the Rabbis did not want to inconvenience one to bring a ladder for that task, considering the unlikelihood he will come to eat it. The gemara then asks that even if we are stringent in this case, perhaps it is nevertheless unnecessary when chametz fell into a pit (from which it will not “fall up”). Then again, suggests the gemara, maybe the person will go down to the pit and eat the chametz.
The Rambam[6] and Shulchan Aruch[7] rule stringently on the question of the rafters. Regarding the pit, they are lenient as long as one does bitul. The Beit Yosef[8] explains that by doing bitul, one lowers the issue to a maximum of a Rabbinic-level problem, and then one need not remove the chametz in this case, which the gemara left as an unsolved question. We do not make him remove that chametz in that case because it would take a lot of toil to get the chametz, and the fact that it is out of easy access makes this case similar to the aforementioned example of rubble.[9] (One cannot purposely put chametz into such a situation.[10])
In describing the example of the rafters, where one must go to the trouble of removing it, the Rambam and Shulchan Aruch talk about a k’zayit[11] of chametz. Some poskim say that if there is less than a k’zayit of this semi-accessible chametz, there is no need to go to the trouble of removing it.[12] Anyway, all sources indicate that if the chametz is in a place that is inaccessible during Pesach and there is significant difficulty getting to it before Pesach, one may rely upon bitul chametz (which we anyway perform as a matter of course) and leave it where it is.
Nonetheless, we are aware that many (if not most) of us seem to be more stringent on ourselves in these matters than Halacha requires. Why isn’t Halacha good enough for us? One source or rationalization for the fixation with perfection in our Pesach cleaning is the following: “People have the practice of scraping walls and chairs that chametz touched, and they have what to rely upon [for being arguably needlessly stringent], and if there is chametz in a crevice that one cannot reach, he should put a little cement over it.”[13] Based on this type of approach, it is common for many normal people to do more than is halachically required and remove every piece or even trace of chametz from various places. So, for instance, if you spend several minutes reaching into the recesses of your sofa to get out chametz, you are more machmir than required, but you are also in good company. Even chumrot should have limits, but these are hard to delineate.