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Rookie quarterback Robert Griffin III’s comfort level in the Washington Redskins’ offense has gradually increased, and as it does, he moves closer toward filling the role of franchise savior.

But tight end Chris Cooley cautions that regardless of Griffin’s impressive athleticism, throwing ability and intelligence, the Redskins face slim chances for success if they’re expecting their prized signal caller to carry the team.

The ninth-year veteran doesn’t deny the fact that Griffin is a rare talent, but after three weeks of offseason practices, Cooley has concluded that the entire offense must assume responsibility for the unit’s success.

“The biggest thing as far as the line and skill positions is to be right,” Cooley said Thursday, shortly after Griffin and the offense wrapped up OTAs with an impressive practice session. “There are specific rules in our offense, and there are specific ways plays are run, and we’ve been unsuccessful over the last couple years because you can look back at plays and you can say, ‘This is great except for one or two guys.’ We can’t be wrong.”

A two-time Pro Bowl tight end, Cooley has seen just about everything in Washington. He has played with seven different starters during his career. The group ranges from young, inexperienced quarterbacks such as Patrick Ramsey and Jason Campbell, to established veterans such as Mark Brunell and Donovan McNabb. But during Cooley’s nine seasons, Washington has made the playoffs only twice (2005 and 2007).

None of those seven starting quarterbacks boasted the rare blend of athleticism and elite talent that Griffin possesses. But Cooley knows one player can only do so much.

“We’ve been part of it long enough that we have to be where we’re supposed to be,” Cooley said, referring to himself and his veteran offensive teammates. “We have to run the routes the way they’re coached. We have to block the protections the way they’re coached. We can’t ask [Griffin] to be running around, making all kinds of plays.”

Griffin has worked to quickly earn the veteran players’ confidence and hopes to provide the boost that the long-suffering franchise desperately needs. He relishes the role, but also craves his teammates’ support, on and off the field from his teammates.

“I want them to believe in me so we can go out and win together,” Griffin said. “Because without them we can’t do it. I can’t snap the ball to myself, throw it and catch it. I need other people out there to help me.”

The Redskins addressed their need for additional playmakers, signing wide receivers Pierre Garcon and Josh Morgan, who paired with Cooley, fellow tight end Fred Davis, and holdover receivers Santana Moss, Anthony Armstrong and Leonard Hankerson, should give Griffin plenty of weapons.

There are questions about the offensive line, where left guard Kory Lichtensteiger is coming off of a torn ACL and MCL, and right tackle Jammal Brown is working his way back from a season-ending hip injury. The running back position also presents some uncertainty, with Tim Hightower coming off of a torn ACL.

Breakdowns along the line and in pass protection, and an inconsistent running game could hamper Washington’s offense. But coach Mike Shanahan has said one of the positives that Griffin offers is his ability to make an “off-schedule play,” (improvising on a busted play and turning nothing into something). That could help mask some problems on offense. But not entirely, says Cooley, who believes improvisation isn’t always the best thing.

“I think yes and no,” he said. “Yes, the idea of an off-schedule play is always a key in the NFL. But that’s something that frustrates a lot of coaches and will sometimes frustrate players. You’ll scheme this whole game and then all a sudden the quarterback or someone makes an off-schedule play that shouldn’t happen. Robert’s the kind of guy that can do those things. But for us to be a team that consistently wins, we have to have him doing the things we want him to do.”

More on the Redskins:

Griffin gets up to speed quickly

Shanahan eager for camp in Richmond

Wilson, Hankerson won’t be full speed until training camp