For those not aware, packing the court in this context refers to expanding the size of the U.S. Supreme Court so that whoever's in power can nominate judges they prefer to the newly-created seats, thereby creating a favorable majority for them where there might not have been one previously. It was attempted once in 1937, but failed, and has not been attempted since.
As for term limits, Supreme Court justices have none; the position is for life. The reasoning for this is primarily so that they can't be influenced as easily for political gain, as they've already achieved the final step in their careers.
Personally, the concept of court-packing has worried me no matter who does it, because from what I can tell (though granted I've not researched this), the Supreme Court has thus far done a decent job of avoiding partisanship; I'm concerned packing the courts would damage this precedent. I do believe that term limits could work, though I suspect they'd require a clause prohibiting justices from holding any jobs after their term expires, lest they become politically influenced by down-the-line job offers.
That said, what's your take?
(By the way, CGP Grey has a great video on some parts of the Supreme Court if you're interested in learning more about it)