How would you or any of us know how long any club is interested in any player before making a move? All we know is that when Spurs finally made a move for Cahill, Chelsea immediately followed suit (or perhaps even made their move just before us).
Besides all which, in the specific context of whether signing Cahill would have meant qualifying for the Champions League in 2011-12 (which is what this discussion is about, after all), it's arguable that Ryan Nelsen was no less dependable and capable an addition to the squad than Cahill would have been. Of course, Cahill had relative youth on his side and has since matured into an excellent Premier League central defender. But at the time, there was little to choose between them.