"If I don't get that timeout back, I'm screwed, and I'm getting fired!" he said, hollering at the referees as he pointed back toward owner Stephen Ross' suite.
From that moment forward, at 3:46 p.m. ET, as an eight-point lead shrunk to a tie and eventually to an overtime loss, the Dolphins would experience a 39-minute span that competes with the darkest, strangest times in team history.
For the moment, Sparano's expectations of his job security proved false. Sources indicated late Sunday that he wasn't to be immediately fired, although nothing at this point feels secure. Nothing, as indicated during those 39 minutes, is predictable.
Instead, the Dolphins' situation has derailed in a way difficult for anyone to explain, and it has become so strange, so surreal, that it's hard to know who to blame or where the source of this derailment began.
Consider one scene in particular:
During the Broncos' tying touchdown, one side of Sun Life Stadium began to chant "Tebow! Tebow! Tebow!" -- while the other side started an anti-Tebow equivalent. A superficial explanation, like the one provided by linebacker Jason Taylor, might seem reasonable enough.
"He's a polarizing figure," Taylor said. "He's had a lot of success here in the state of Florida. He has a lot of followings, which is fine."
But Taylor, who earlier in the game raised his arms to motivate the crowd to keep the chant going, is missing a bigger point. As it pertains to the Dolphins, the ire was never really about Tebow. It was about the team -- the home team -- that honored its visiting conqueror. Tebow was nothing more than an unknowing aggravator of a much deeper dysfunction that currently exists within the organization.
This was about a coaching staff (and the players that support it) on life support, irked by management's decision to hold a day in honor of Tebow and the University of Florida -- but also realizing if it produced more wins, then cheap endorsements like this one would be unnecessary.
It is about an owner (and the business side that supports him) that keeps making public hiccups, even if deep down that owner sincerely wants what is best for this organization and this team.
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On Sunday, when Sparano pointed toward Ross' owners suite as he made his job insecurity known to everyone around, the owner wasn't up there. He was instead headed down to the sidelines, where he expected to celebrate a win.
But instead of a celebration, Ross stood smiling next to former Florida coach Urban Meyer, as Meyer's former quarterback from his days with the Gators began dismantling Ross' team in a surreal comeback.
Meyer's wife and son stood next to them, cheering from the Dolphins' sideline as Tebow worked his magic -- all while CBS' cameras focused on Ross' smiling face.
Did he mean anything wrong by this? No. He was caught in an awkward spot, and rather than excusing himself from the conversation, he perhaps mistakenly tried to act nonchalant about the situation playing out in front of him as Tebow orchestrated a 15-point comeback.
But Ross put himself in that awkward spot. His people created this Gator Day. They invited these fans -- and Meyer -- into their stadium for Tebow's return to Florida, so any resulting backlash from it also falls on him.
So is he to blame for all of this? Not entirely, of course. Like the premise of this Gator Day promotion itself (to sell more unwanted tickets), Ross wouldn't have been in this desperate situation had it not been for the failures of the product on the field.
All of these embarrassments -- on and off the field -- must be owned by everyone within the organization. And while it might be difficult to differentiate where to place the blame, this ugly cycle of the chicken and the egg must eventually be forced to an end.
With each day, it becomes more obvious that change is necessary. The coach's tensions are seeping into his game-day decisions, and the business side's desperation to remedy their own situation is creating embarrassments like the one suffered Sunday.
It seems difficult at this point to expect Sparano to remain in Miami much longer, even if this isn't entirely his fault. Sparano is a good man in the middle of a mess much bigger than him, but it'd be tough for anyone to argue with much conviction that the changes won't start with him.
This, though, is about much, much more. It's about more than a coach. It's about more than his players. It's about more than a Gator Day. It's about more than one loss. This is about a team in need of major evaluations from top to bottom.
During those final 39 minutes, many people within the organization put themselves into strange positions to contribute to the awkwardness of the day.
So if the Dolphins want to find a way to resolve the ongoing slew of dysfunction that has this team obviously headed in the wrong direction, it's going to be important for many people to evaluate how they contributed to this surreal conclusion.
Is any single person to blame for those final 39 minutes? No. Not on this day.
On this day, everyone was to blame.