CHICAGO (AP) — The little engine that could finally threw a gear.

The Chicago Bulls might have been the most heartwarming tale going this postseason, but it’s over. Unlike the bedtime story, fumes and spare parts get you only so far in the NBA. It was always a matter of when — not if — they’d fall apart.

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Go back and take a look at what happened in the third quarter of their Eastern Conference semifinal Monday night against the Miami Heat, or better yet, don’t. It was about as ugly as you’d imagine. The Bulls scored exactly nine points in the period, an all-time franchise low.

At various times in the final quarter, Chicago had Nazr Mohammed, Daequan Cook, Malcolm Thomas, Marquis Teague and 35-year-old Rip Hamilton on the floor. What’s scary isn’t that some NBA fans had no idea that any or all of that group was in the league; rather, it’s that many of those same fans wouldn’t recognize the guys they were supposed to be spelling.

The Bulls wound up shooting 26 percent and totaled just 65 points by the end of Game 4, another team record for futility. Yet they probably had no business getting that many, let alone this far in the playoffs.

“We’re kind of putting screws and bandages everywhere,” said forward Taj Gibson, another backup pressed into regular service. “It’s frustrating. Every night and every day.

“It’s rough. It’s really rough,” he added a moment later. “I wish I could explain how I’m feeling right now. How everybody in this locker room is feeling now.”

Actually, there’s no need for a lengthy explanation when a glance will do. Gibson had icepacks covering both knees as he talked. Across the room, Joakim Noah had his right foot (plantar fasciitis) submerged in a bucket of ice. Next to him, Nate Robinson had an icepack covering his left shoulder. The players who hadn’t left in a hurry to lick their wounds at home were still lined up in the trainer’s room, awaiting their turns.

Every team has to cope with injuries, but what happened to the Bulls and coach Tom Thibodeau this season gives the phrase new meaning. His best player, Derrick Rose, the league’s MVP in 2011, was a scratch at the start because of knee surgery, and despite a doctor’s note clearing him to return in March, he never did. Somehow, the Bulls won 45 regular-season games, then even more surprising, beat back Brooklyn in the first round.

Naturally, things only got worse. Chicago’s second-best offensive player, Luol Deng, who played all season with a variety of hurts, has missed the last six playoff games; the Bulls’ best perimeter defender, Kirk Heinrich, similarly battling injuries for months, has been out for the last seven.

Now the Bulls head to Miami down 3-1, where this series will end — officially, but mercifully, too.

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“They’re in a tough situation,” LeBron James said — not that it stopped him from dropping 27 points on Chicago’s wearied defenders. “They’ve had some injuries and illnesses and whatever’s going on. They don’t have their full roster, but that’s not for us to worry about.”

That was Thibodeau’s worry all season, and the jury could be out for a while deciding whether he treated the players available at any given moment like a chess master or a meat grinder. The team’s unofficial motto became “Next Man Up!” — the Bulls left a placard with the slogan on every seat in the arena Monday night — but “Next Man Down!’ might turn out to be more accurate in the long run.

Thibodeau possesses one of the league’s best defensive minds, and the effort he coaxed, mostly from a bench long on second-stringers, was something to behold. In what might have been his final motivational ploy for this season, Thibodeau put out a revised lineup just moments before Game 4 with Deng listed as “active,” even though he wasn’t long out of a hospital bed. The coach also reached deep into his doghouse and finally tossed a few minutes to Hamilton, who like Robinson, shoots the ball without conscience and is a defensive liability.

Neither is Thibodeau’s kind of player. Whether the pair returns remains to be seen, though you could say the same about a few more of the youngsters and castoffs the coach used to great effect. The more important question is whether the front-liners — Rose, Deng, Heinrich and Noah, who’s played relentlessly despite the foot injury — will continue to entrust their careers to a coach who won’t, or can’t, ever take his foot off the throttle.

Afterward, Thibodeau was asked whether the Bulls’ performance was proof they’d simply “run out of steam.”

“No,” he replied. “I think the thing is they’re (Heat) a great team. We have to come out with great intensity — but we also have to make shots.”

The Bulls never really had enough guys who could do that — shoot — to seriously contend. They came back down 3-1 against the Nets and stole the first game of this series with toughness and intensity, but they’re short on those qualities now, and exhausted to boot.

“There’s a lot left in the tank,” Robinson said bravely. “Down 3-1, you never know. Take it to Game 7 and we end up winning, it’s going to be a beautiful story to tell my kids one day.”

Or not.

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