Referee John Petrone checks his notes during an NFL preseason game. (JONATHAN ERNST/REUTERS)

Rarely, it seems, have some NFL players, coaches and fans longed so much to see yellow flags tossed and penalty announcements made by Ed Hochuli, Mike Carey and the other referees they have spent countless Sundays disparaging in the past.

The NFL season begins this week and, barring a last-minute breakthrough in the negotiations that resumed late in the week but stalled again Saturday, will start with the sport’s regular referees far away from the field.

The league used replacement officials during the preseason and has said that it intends to keep doing so if needed during the regular season, which begins Wednesday night in East Rutherford, N.J., with a nationally televised game between the New York Giants, the defending Super Bowl champions, and the Dallas Cowboys. There is a full slate of opening-weekend games scheduled for next Sunday, including the Washington Redskins playing at New Orleans.

The preseason included its share of officiating gaffes. And after NFL Commissioner Roger Goodell wrote a letter to fans in advance of the season that touched on topics of player health and safety, Cleveland Browns linebacker Scott Fujita wrote Friday on Twitter: “Dear NFL, Thank you for your letter to fans on player safety [and] the integrity of the game. Now can the refs please come back to work? Thanks.”

Fujita perhaps is not a neutral observer, given that he is among the four players suspended by Goodell in connection with the bounty scandal involving the Saints. But he is not alone. Many players and media members were sharply critical of the work of the replacement officials during the preseason. Minnesota Vikings punter Chris Kluwe called the replacement officials “horrible” and the situation “kind of embarrassing” via Twitter. Giants wide receiver Victor Cruz told the New York Times that an officiating mistake earlier in the preseason was “mind-boggling.”

A steep learning curve

Other reactions have been more measured.

“It would be different if you were breaking in one new guy, two new guys on a crew,” veteran Redskins linebacker London Fletcher said last week. “But you’ve got whole crews that are new to the pro game of football. It’s just officiated totally different. Obviously there are some calls that you look and see and you’re like, ‘Man, wow.’ But for us, both teams have to deal with it. It’s just something you’ve got to deal with. Hopefully they’ll get better as the season goes on and the more experience they get. It’s really like a rookie coming into the NFL. You hope they improve each and every week.”

There are hopes that a deal could be struck between the league and the NFL Referees Association in time to have the regular officials back for the opening of the season.

The league informed its teams in a memo Wednesday that it intended to begin the season with the replacement officials on the field. According to that memo, there remained considerable differences between the two sides on economic issues, including salary and pension, and non-economic matters, such as the league’s desire to increase the number of officials and make some of them full-time employees.

Negotiations resumed late in the week and the two sides met Saturday, but the referees association announced that no deal was struck and it does not expect its members to be on the field for the opening week of regular season games.

The NFL issued a written statement Saturday confirming the breakdown in negotiations and saying it is “proceeding with the replacement officials.”

“For the good of the game . . . we deserve to have the best players on the field and we deserve as fans to have the best officials on the field, too,” said Mike Pereira, the league’s former vice president of officiating. “You can say that people don’t go to see the officials work, and that’s true. But then again, we don’t have a game without officials. So they’re a hugely important element of this game that we’re involved in.”

Pereira, now an NFL analyst for Fox, said during a conference call with reporters last week that the problems of the replacement officials during the preseason will be “magnified” when the regular season begins and the intensity of the players and coaches is amplified. Part of the issue for the officials, Pereira said, is knowing the NFL’s complex and unique rules and going through the proper mechanics of enforcing them.

“Hey, listen, the regular guys make bad calls, too,” Pereira said. “Let’s don’t discount that. But I do think with the regular guys that you never question a penalty enforcement or a timing issue, those types of things that you can expect perfection from and you do get. I don’t think that’s the case here, and I think that’s going to be an issue for [the replacement officials]. And I think also player safety. . . . They’re not used to seeing that type of hit with that type of speed, and I think it’s just a huge adjustment that they have to make.”

Concerns about safety

Former Cowboys quarterback Troy Aikman said he, too, worries about the player-safety issue.

“I haven’t seen a flag for an illegal hit on a quarterback yet, of the [preseason] games that I’ve seen, and yet I’ve seen them in each game that I’ve watched,” Aikman said.

The NFL Players Association has raised the safety issue, with the lockout of the game officials coming at a time when the league has toughed its rules on illegal hits in recent years to try to curb the rate and severity of concussions suffered by players.

The league has defended the performance of the replacement officials, who were culled largely from the lower-tier college ranks. But there was plenty of scrutiny on their preseason mistakes. In Redskins games alone, the replacement officials called a touchback on a punt that, after a reversal on a replay review, ended up being spotted on the 4-yard line, and in another instance stopped the game for a replay review, then walked back on the field and announced they were going to take another look at the replay.

“There’s got to be some concern on the coaches’ parts . . . and the people that are watching from the sideline: ‘Okay, now are we going to challenge how this rule is administered?’ ” Aikman said. “That becomes another layer of problems and concerns for the [coaching] staff.”

The NFL used replacement officials for a week of regular season games in 2001. Tony Dungy, the former coach of the Tampa Bay Buccaneers and Indianapolis Colts, said the experience “really wasn’t too bad” then but could be more trying this time around.

“These are not the same cast of characters,” Dungy said. “I’m not sure how this is going to go. The good thing about it for the coaches, now they’ve had four weeks to see it. They’ll know how these games have been called. They’ll be able to adjust accordingly.”

The sport’s instant-replay rules have been expanded in recent seasons, potentially decreasing the chances of the officials making an error that decides the outcome of a game. In addition to coaches having replay challenges, all scoring plays and all plays with a turnover are now subject to automatic replay reviews. Even so, if the lockout of the officials does spill over into the season, league leaders surely will be crossing their fingers that nothing goes too wrong.

“A lot of these referees and crews have been put together from the smaller college ranks,” said Jon Gruden, the former coach of the Oakland Raiders and Buccaneers. “They have never met each other. They have never worked a game together and I think it’s a really great accomplishment for the way that they have maintained order and gotten better on a weekly basis. But I still think it’s going to be a challenge.”

Staff writer Rick Maese contributed to this report.