Even though you could say that Tottenham still has hope of finishing fourth in the standings at the end of the season, I personally am not sure that Tottenham will be able to get a ticket to the Champions League next season
Nobody can be sure about future and nobody can be sure about what Tottenham can do in rest of season as well as their final ranking in Premier League.
because the competition is very tight, for the first and second places Arsenal and Manchester city can be said to be safe. but for the third and fourth positions I can't be sure, even though Chelsea and Liverpool are currently struggling in the mid-table but I still put them in the top four list this season, even though Liverpool and Chelsea are being hit by a hurricane of injuries but I'm still optimistic Liverpool can compete with Manchester United, Newcastle and Tottenham to get tickets to the Champions League next season.
The competition is extremely tight and it becomes more challenging for involved clubs with a sudden participation of Newcastle United. They are not a familiar name in top four competition but actually joined it in this season.
Tottenham can be in top four because currently their differences with Newcastle United and Manchester United are not too big. It can be covered any time if Tottenham play well and those clubs play bad. Though I believe in Tottenham ability, I agree with you that the competition is tight and Tottenham will have to fight to their last sweats to beat other clubs and be qualified for top four.
In their side, Tottenham must help Son Heung Min solves his performance crisis that is worse than expected. Kane has a good season but Son is different. He has a very disappointed season compares to the past one when he was a winner of the league's top scorer (together with Mohamed Salah from Liverpool).