One of the commoner reasons I hear from conservative Mormon women for not wanting the priesthood is that they already have so much on their plates—so many responsibilities—that the priesthood would just be an extra burden. This complaint is not wholly unjustified. According to sociologists, one of the main challenges faced by women who’ve entered the workforce is that their husbands tend not to pick up a fair share of the domestic duties, so women end up working a “second shift” at home after they get off work. As a result, many working women experience a “double burden” and have less leisure time than their husbands. This holds true even for many women who have relatively progressive husbands and who perceive the domestic work in their households to be evenly divided. (If you measure it empirically, it often is not.) One can certainly imagine something similar happening with the priesthood. Women might take on extra administrative duties and still be expected to run the nursery, teach primary, and clean, cook, and care for the children at home.
But of course, no one would argue that we need to paternalistically protect women from this “double burden” by forbidding them to enter the workforce. That would be silly. For some women a career will be worth the extra work, and others may be able to negotiate a more equitable work-sharing arrangement if they can make their husbands aware of the “second shift” concept. Similarly, for some women holding the priesthood would be well worth any extra burden it imposed. There’s really no reason for overburdened women to oppose having the option of ordination, and I don’t think anyone is asking the Church to make it mandatory.
More importantly, the Church could easily help avert the “double burden” problem if its introduction of female ordination were coupled with an effort to redress the balance of domestic duties. This is one of the advantages of a change in LDS Church policy over the change in US government policy that allowed women to enter the workforce: the LDS Church can exercise much more social control over men’s responses to the change. As with rape, the solution is not to impose constraints on women to prevent their victimization; the solution is to teach men to be fairer, more aware, and more ethical in their treatment of women.