Welcome to Flyertalk and welcome to the TAP forum.

EC261 does protect you here, in that TAP will need to offer some sort of same day service, but probably with a connection. When I had the exact same problem with TAP, the website only initially offered movement of dates, but when calling up there were a heap of other options involving jetBlue and United services. In the end I chose to go SFO-BOS-LIS, for which the timing were pretty good. SFO-BOS was jetBlue, then TAP from there. If you play around with the TAP website, you should see the sort of options that are open to you. But just come up with an alternative that is OK for you, run that past the telephone agents, and if they can't offer it, get them to dig out alternatives.

Separate tickets isn't always a good idea, but you did have a 2 day break and normally that would work fine. If you give the dates then we can give more precise guidance.