Let's say you are walking down a street, finishing off chips from a polystyrene container when you notice, nestling among the autumnal leaves, a similar container previously discarded by a third party. Tut, tut, you think to yourself, how careless and inconsiderate. As you are congratulating yourself on your moral superiority the wind catches your, now empty, container and deposits it beside the other one. You are distracted by a car passing and when you look down again you aren't quite sure which container is yours. First poser is, what do you do? a) Walk on, b) Pick up one container and put it in the bin or c) Pick up both.
I'd suggest that the option which feels intuitively correct is c). It doesn't "feel" right to just pick one and leave another there and you can kiss goodbye to your moral superiority if you walk on, leaving both on the ground. This would suggest that there is some sort of obligation to dispose of the other container if it is convenient for you to do so.
Now, rewind the scenario and replay without the gust of wind. Your options are a) to bend down and pick up the litter or b) walk on. In this version I'd suggest that b) feels correct in which case your intuitions are telling you something different. You don't feel any obligation to dispose of the carton on the ground as it's not your responsibility, even though no significant inconvenience would be involved.
I'm not sure what the correct answer is, whether the proper course of action ought to be governed by responsibility (the deontological approach) or convenience (consequentialist approach), although I lean to the latter, but I think it's clear that an appeal to what seems intuitively correct will not suffice.
There is a school of thought which suggests that rational argument ought to be subject to some sort of final intuitive imprimatur. If the conclusion of your rational argument feels wrong, it must be wrong. One example of this is to be found in Julian Baggini's "The Pig that wanted to be eaten": A thought experiment about a person who has been convinced "by rational argument" (unstated, natch) to indiscriminately kill lots of people as quickly as possible. Baggini suggests that the person should resist, no matter how compelling the argument might seem. But, although he is correct in this particular prescription it is for the wrong reason - if one of your starting principles is "you should not indiscriminately kill lots of people", no rational argument based on this can arrive at the contrary conclusion, it is not the rational argument that is the problem. This is just lazy thinking - It is certainly much easier to simply abandon an argument with an unsettling conclusion instead of doing the hard work of picking apart one's assumptions - and opens up the door to all sorts of irrationalism. There are plenty of things that "feel wrong" but are correct. The world "feels" flat but it isn't. The best use of an intuition is as a check on an argument. If your argument doesn't chime with your intuition, one of them is going to have to go. But if, upon further examination, it seems that there is a plausible cognitive bias or unexamined assumption behind this unease, then it is the intuition which should be junked, not the argument.