Actually, Amanda, in accordance with Portuguese law (paraphrasing my lawyer), you can remain in Portugal even before the actual pre-approval: once your application is submitted and fees are paid, your case is considered “pending”. This means they won’t kick you out of the country after your initial 90-day automatic U.S. tourist visa, but you won’t be able to travel outside Portugal. If you are flying out, leave for a non-Schengen country like U.K., Ireland, U.S., Canada, etc.
Also, there is a bi-lateral agreement still in force between U.S. and Portugal that gives you additional 60-days past 90-day tourist one. I have the text of this treaty referenced in the following thread: U.S. - Portugal bi-lateral treaty.
Between all these, amounting to 150 days after your arrival, you should receive your pre-approval and maybe even an invitation for biometrics if SEF, with its newly-created special task force to clear the backlog of applications, would pick up the pace.