It's definitely a different situation to most other clubs.
We're the club that everyone, the media included, likes to laugh at. We're one of a handful clubs that hasn't been relegated during the Premier League era. We've spent the last decade and a bit mixing it with the top of the league, spending (relatively) big money. We have an AWESOME stadium, good media presence. But we haven't won anything. That makes us an easy target.
Supporters of the bigger teams look down on us for not winning anything, while being scared that we'll take their place.
Supporters of the smaller teams look up at us with jealousy, using anything they can to reassure themselves that, well, their club is just as good as Tottenham.
While we aren't the "evil empire" that ManU or Emirates Marketing Project are, we're never going to be the plucky underdogs. We're no-one's second team, even when we were playing beautiful football under Poch. We're never going to get the sympathy vote that Everton and Villa might get, despite us not being (until recently) much different to them.
That puts any manager into a difficult situation. Win something, finish in the top 4, or be damned. The flip side is that, in the modern era, there aren't many teams with a solid enough base for sustained success. We're one of the few that could.
Or is it just me, as a fan, deluded into thinking we're special?
We are special mate, and without repeating you too much it's that mix of too big to be the underdog, not quite big enough to be elite, worldwide fanbase and the revenue that provides but not money doping, not one of the initial top 4 that got to cash in and create headstart with PL/CL but also not one who let their seat at table go.
Everytime I see how rabid the media, other supporters get about us, Kane, ref decisions (Brighton game example), I remember the quote -> it's better to be hated than irrelevant