Yes, it is a possible option for the United States to make both men and women draft eligible. The media puts a large emphasize on equality in this day and age, in salary, occupation, and other areas of the like. In addition, both men and women live in the United States. With traditional gender roles in flux I feel that it is completely reasonable that both genders should be eligible to protect it.
I thought something like this already existed. I was under the impression that America was already on to something like this. Hopefully, women who want to be drafted are drafted, and no one pregnant has to be drafted in. There are downsides but if America thinks were going to run out of men, then have the draft be genderless, as long as they aren't forcing women to run out first.
Norway has now followed the lead of several other countries in adding women to the draft. This might be a good way for the US to go as well. In terms of gender equality, participation in the armed forces should be equal. Women have access to some intelligence gathering men don't and a balanced military is probably a healthier one.
Reinstating the draft as well as having to make ladies to join may possibly motivate communities to experience a risk in these wars. We will need to speculate what is the reason, as well as information about how, we head to conflict, as well as who makes a decision to send our people into harm's way.