"Long term answer" implies that he can be the every day starting shooting guard for years to come.
Right now, Avery has shown himself to be a stupendous, tenacious defender who, due to his size, is probably best suited to hounding opposing point guards rather than shooting guards.
He's also been fairly injury prone in his short career.
Lastly, he's been a rather mediocre offensive player who has had some flashes, most notably a 1-2 month stretch in the 2012 season where his jumpshot was falling and he was developing some nice chemistry with Rondo and scoring at a decent rate with good efficiency.
Overall, I'd say that it's hard for me to feel optimistic that he will be that "long term answer" just because I tend to think that injuries and his overall style of play may force him to be more of a short minutes, "energy guy" type of player, especially when his size is considered. I rather doubt that he'll ever be more than an average player on the offensive end, and I think even that would be an accomplishment.
None of this is to say that I don't think Avery is a really nice player who will be valuable for a while. I just don't know that I'd commit to him being the "long term answer" just because if a better two-way player with more prototypical SG / SF size came along, I'd probably prefer to invest in that player instead.