Could the Giants lure a big-name coach back to the NFL? (Patrick Semansky/AP, Chris Gardner/AP, Kevin C. Cox/Getty Images)

Ben McAdoo was overmatched by being an NFL head coach, particularly on the big New York stage. That became painfully clear as an ever-more-miserable season for the Giants progressed, and it culminated Monday in his firing as part of an organizational housecleaning that also included the ouster of General Manager Jerry Reese.

The Giants’ coaching job is a big-boy job.

Their next coach, accordingly, must be a big-boy coach.

That could mean luring Nick Saban away from Alabama, if Saban is willing to return to the NFL and right the wrongs from his unsuccessful stint with the Miami Dolphins. It could mean making an effort to pry Jim Harbaugh from Michigan. It could mean bringing back Bill Cowher to an NFL sideline, if Cowher is willing to leave the comforts of a network TV studio-analyst job and the Giants believe he’s not too far removed from his coaching heyday with the Pittsburgh Steelers.

It could mean giving Josh McDaniels another NFL head coaching chance, following his failure with the Denver Broncos and the recent rehabilitation of his offensive-genius reputation as a coordinator in New England. It could mean hiring any of a number of other coaches.

But it cannot mean taking another leap of faith on another unproven head coaching commodity like McAdoo, who was elevated from offensive coordinator to head coach before last season following the exit of a two-time Super Bowl-winning coach, Tom Coughlin. The Giants reached the playoffs last season with McAdoo as a rookie head coach. But things fell apart this season, as the Giants have tumbled to a record of 2-10.

“We’ve had an embarrassing season,” Giants co-owner John Mara said at a news conference Monday. “I think most people that know me know how painful that is to me and know how committed I am to try to put a winning team back on the field. I know our fans are suffering. But I’m suffering more. I guarantee you that right now. We’ve gotten to the point where we just felt like we had to make wholesale changes. And that’s what we’ve done.”

The amount of respect that McAdoo commanded from his players was called into question when he suspended two players this season for violating team rules and when analysts in the media criticized the effort level of Giants players during games. McAdoo’s inability to deal with the internal politics and public relations aspects of the job were evident during his clumsy handling last week of the Eli Manning situation.

Coaching in New York is not a great place for on-the-job training.

Saban and Cowher have been linked to the Giants’ coaching job in the past. There are several issues with Saban, who is overseeing a college football dynasty and about to participate in another playoff. Even if he would be willing to consider a return to the NFL, he would need to be given a monstrous contract and he probably would seek control over the roster.

That’s generally not how the Giants do business. They are a tradition-laden franchise that believes in the traditional arrangement of dividing powers between a general manager and a coach.

Mara was asked about that Monday and said: “My very strong preference is to maintain that traditional separation. But again, I would never say never if the right candidate was there.”

That wouldn’t be a problem for Cowher, who was a Super Bowl-winning coach in Pittsburgh. But he hasn’t coached since 2006. The Giants would have to decide if that disqualifies him, even if he would be willing to consider a return.

Harbaugh is an intriguing possibility because he did have NFL success in San Francisco, taking the 49ers to three straight NFC title games and reaching a Super Bowl. But he is in his supposed dream job at Michigan. There were issues in San Francisco with his ability to coexist peacefully with the front office, and his career-long propensity has been to move on to the next job after a few years.

McDaniels is well regarded as a head coaching candidate again, thanks to his success in his latest stint with the Patriots. The coaching wizardry of McDaniels and his boss, Patriots Coach Bill Belichick, was on vivid display last season when New England went 3-1 during Tom Brady’s Deflategate suspension en route to another Super Bowl title.

McDaniels can draw on his experiences from his turbulent 28-game head coaching stint with the Broncos in 2009 and 2010. The thickness of his skin cannot be questioned, as anyone who witnessed Brady screaming at him on the Patriots’ sideline Sunday can attest.

Other candidates undoubtedly will be mentioned, perhaps including college coaches such as Stanford’s David Shaw and NFL assistants such as defensive coordinators Teryl Austin of Detroit, Mike Smith of Tampa Bay, Jim Schwartz of Philadelphia, Mike Vrabel of Houston and Matt Patricia of the Patriots, along with Pittsburgh offensive coordinator Todd Haley and Kansas City special teams coach Dave Toub. The Giants said that Steve Spagnuolo, who was elevated from defensive coordinator to interim head coach Monday, will be a candidate.

Mara said a lack of previous head coaching experience would not eliminate a candidate.

“It just depends on the candidate,” Mara said. “There are a number of new head coaches that have been very successful in the league this year. So you can’t shy away from them. If you think you have the right guy, you’ve got to go for it.”

For now, at least, the Giants’ plan is to hire a GM and then move on to their coaching search. Ernie Accorsi, the team’s general manager before Reese, agreed to serve as a consultant in the current GM search.

“It’s really been the perfect storm this year,” Mara said. “Everything that could have gone wrong has gone wrong so far this season. And it’s just one of those things you have to live through and suck it up and make whatever changes you have to make and go on.”

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