The morning after pill is given to women within 24 hours of unprotected intercourse. One pill is taken immediately, the second exactly 12 hours later. If conception has taken place, the pill will prevent the fertilised egg from nestling in the lining of the womb. The pill has some serious side-effects. Because it's a high dose of the female hormone progesterone, it causes nausea and vomiting. It also disrupts the menstrual cycle.
A number of considerations come into play when this pill is given over-the-counter. In the UK, it is only handed out from pharmacies. You can't buy it in a supermarket. The pharmacist is trained to ascertain whether it is appropriate for the woman asking for the pill to have it in the first place. I am unfamiliar with the US regulations.
As the pill is intended to stop the fertilised egg from developing further, it is argued that you are terminating a pregnancy, even if it's less than 24 hours old. There are people who are opposed to abortion, at any stage of pregnancy and who are therefore unhappy to see the availability of this pill widened.
Others will make the point that it will be seen as an excuse for having unprotected sex, not wearing a condom, not go on the anti-conceptive pill or use another method of contraception. Apart from the fact that this is an emergency measure, it also does nothing to prevent the spread of sexually transmitted disease.
I am broadly in favour of having the pill available without a prescription, using the regime that has been in place in the UK for a few years now. Accidents happen, worse than that, so does rape. Over and above that, it is argued that it should not be given to children. In the UK, there is a large problem with teenage pregnancies (under 16), and education should also be improved. There is a long way to go with this yet.