Giants quarterback J.J. McCarthy runs with the ball against New Orleans...

Giants quarterback J.J. McCarthy runs with the ball against New Orleans Saints linebacker Pete Werner during the fourth quarter at MetLife Stadium on Sunday. Credit: Brad Penner

This probably isn’t what John Harbaugh thought would happen when he made the seemingly innocuous call to switch quarterbacks late in Sunday’s game against the Saints. The Giants trailed by 24 points and he surely just wanted to salvage some positives from the lost afternoon and give J.J. McCarthy a few actual reps with the offense.

It turned into something else very quickly, however, when McCarthy nearly rallied the Giants all the way back.

So Harbaugh has a quarterback decision to make.

“It starts right now,” he said of the deliberations that will take place in his head, in his heart and with his staff as he tries to figure out who’ll start against the Texans in Houston on Sunday.

But that’s not quite true, even given the pensive gaze and cinematic pause Harbaugh gave to punctuate the statement as he looked off into the future.

It was just as much of a coaching fib as it was when he said, just a few minutes before officially beginning the clock on his considerations, that the issue shouldn’t be “up for discussion or conversation” in such proximity to the end of the kind of wild game the Giants had experienced in their 34-27 loss.

The reality is that the latest events at MetLife Stadium, while dramatic, were simply one element in a situation that has been churning below the surface for this organization through the feel-good times of a few wins and a tie.

It didn’t “start right now,” as Harbaugh said on Sunday afternoon. It started when the Giants traded for McCarthy after Jaxson Dart suffered a season-ending knee injury last month and pitted him against backup-turned-starter Jameis Winston for the chance to lead this team.

It started when the Giants realized that although Winston would be able to navigate them through some short stints in their schedule as a veteran, his erratic play eventually would cost them games if they opted to depend on him for the near entirety of a season.

Harbaugh, in other words, has had plenty of time to think about this. So much so that he has to already have made up his mind.

The question really isn’t when the decision-making process starts, as Harbaugh suggested. It’s when it ends.

That will come when Harbaugh names McCarthy the starter.

It’s a result that feels as inevitable today as it did the moment the former top-10 pick arrived here from Minnesota. It’s also a move that was accelerated by his 243 passing yards that led three scoring drives — all in the fourth quarter — and fell 14 yards shy of a fourth that could have won the Giants a comeback for the ages.

Such an announcement could happen this week. It could be during the bye on the other side of the trip to Houston. It could be a few weeks from now if Harbaugh wants to really drag things out and give Winston more opportunities at the risk of allowing this golden opportunity to stay atop a weak division to slip away.

But McCarthy eventually will take over.

It’s why Harbaugh brought him here.

“I hope I just showed that I can do my job at a high enough level that they can trust me out there,” McCarthy said after turning what felt like mop-up duty in a game with a 24-point deficit and 11:31 left into one that came down to a fourth-down incompletion in the end zone from the 14 with six seconds left.

“At the end of the day, we didn’t win the game, so we have to be better. I have to be better and figure out ways that we can pull this thing out next time.”

Oh, there absolutely will be a next time.

The fans who stayed made it clear whom they want moving forward. After groaning over every errant Winston pass for most of the day, they were firmly behind McCarthy’s comeback attempt, especially as it pertained to whizzing the ball deep down the field to Malik Nabers and Isaiah Likely. Even Charlie Jones, whose costly fumble on a kickoff return in the first half had turned the momentum of the game over to the Saints, got a highlight grab. Those are receivers to whom McCarthy had never thrown live passes before Sunday.

“You feel them every single snap,” McCarthy said of the crowd. “Being able to lock in on my play, that’s ultimately the only thing I was thinking about, but you definitely felt them.”

Even Winston was excited for McCarthy.

“Man, he was able to rally us up, and he did a great job,” he said. “I was proud of him, proud of what he did.”

Winston also said he wanted to keep playing. He still does. It’ll be up to Harbaugh to decide when he doesn’t any longer.

Winston and McCarthy said they have confidence that Harbaugh will make the best decision for the team.

Harbaugh said he has “no problem” with Winston despite his up-and-down time as the team’s starter (which was mostly down with two ugly interceptions on Sunday in the team’s first loss since Week 2, when Dart got hurt).

As for McCarthy he said the reliever did a “heck of a job” while conceding that his performance came in “desperation” mode, which is “different than normal football.”

He did add that McCarthy was running the full offense when he was out there, the first time he has done that after appearing on gimmick snaps and package plays previously.

“I felt at home in terms of playing quarterback, being able to run the whole show and make the protection calls and be able to throw the ball a little bit,” McCarthy said. “It was a lot of fun to be out there with this group and to be able to attack this next week no matter what happens.”

Or, as we all know the case to be, when it happens.

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