First of all, this looks like a strong play.
But you asked for reasons not to play it. So I'll try.
The schedule. Spurs are on two days rest (and a trip from Portugal) and will have to face Braga again two days after this match. They won't be too sharp. Even though it's the FA cup, it has the slight flavor of a sandwich game for them. Add to that that Chelsea has only allowed two goals in its last eight (!) home games, and I could see a zero on one end of the scoreline.
Chelsea, of course, has just reached the next round of the Champions League, beating Porto. They're also still in the hunt for the Premiership title, even though that's not looking too good. Previously, when a team has fought on these three fronts, which results in an overly crowded schedule, they have sometimes chosen to let the FA cup go. I don't think that Chelsea will be so inclined, because Mourinho doesn't think that way.
Both clubs are off a European high, which makes this game a bit of a downer, as important as it may be. Another minor factor that could lower the interest level.
In a way this is the first real FA cup match of the season for both teams. Until this point, those matches were mostly warm-ups. Added to the fatigue, and possible lack of interest, that could mean a careful strategy, with greater emphasis on defense, resulting in low scoring game. This could be one boring game. Maybe 1-0 or at the most 2-0 to Chelsea.
How's that for a game I'm not playing?
GL.