When the 2009 season ended, John Mara said it would take a while for him to get over the bitter taste of the way that campaign closed out. Then today, when I spoke with the Giants president and CEO just a few minutes ago, he again noted that he hasn’t quite gotten the bad taste out of his mouth.

So I asked him the perfect softball question as a follow-up:

Is there anything this year that can mouthwash away that bad taste?

“Yes,” he said laughing. “Standing on a platform in Dallas Cowboys Stadium in February being handed the trophy. That would do it.”

Does Mara think he has the team to get that done? He didn’t make any guarantees, but he also had the appropriate level of optimism as the team heads to training camp.

“I think that we have as good a chance as anybody,” he said. “I like our team. I think we have depth at certain positions. I think we have a couple of question marks, but I think every team goes into every season with that. I think the talent, particularly in our division, is so evenly spread out that anybody has a chance to win it. But I think our chances are as good as anybody’s.”

A few other points of interest from our conversation:

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Regarding Tom Coughlin’s future with the Giants and whether or not it is tied to how the team performs this season, Mara said that’s more a media idea than a reality. “I don’t know that it’s any more important than any other year,” he said of the upcoming season. “That seems to be a theme with a lot of the media, but I don’t know that it’s any more important. One of the reasons we hired him as a coach in the first place was that he looks at every season as his most important season ever. That was one of the things that attracted us to him in the first place, that the most important thing to him was winning no matter what the circumstances. So I don’t look at it … It’s an important year for all of us, particularly going into a new stadium, but I wouldn’t say that this season is any more important than any other in terms of Tom Coughlin.”

On the two unsigned draft picks, first-rounder Jason Pierre-Paul and second-rounder Linval Joseph, Mara also had optimism. “I think they’ll be signed,” he said. “It’s been very slow around the league and everybody, teams and agents included, is waiting to see what the others are going to do, waiting to see where the various players slot in. I think you’ll see it happen, hopefully before the first practice on Sunday but if it ends up being a few days after, so be it.”

“I think we’re in a situation where a lot of guys haven’t signed for whatever reason and I think the agents are very hesitant to make commitments for whatever reason,” he added. “You may see a few more holdouts than usual, but I’m not going to lose any sleep over that. I think we’ll get them both signed before too long.”

And finally, Mara said that the pressure of establishing a winning atmosphere at the New Meadowlands Stadium is probably felt more by ownership and management than by the guys who will be on the field. “I think probably we feel it a little bit more because we are going into a new stadium and with the PSL program and with all the money that a lot of people have paid to be in the new stadium,” he said. “I always feel pressure to win every year no matter what the circumstances, just because it’s so important to me and so important to my family. But this year we might feel it a little bit more because of this new stadium. I think in terms of the players and the coaching staff, they’re all professionals and they want to win every year. I don’t know that it adds any pressure on them.”

I said “and finally” in the last paragraph, but that may have been an exaggeration. This is the “and finally” from our conversation. It’s about stadium naming rights. I asked if there was any movement in terms of acquiring a naming sponsor. “Nothing that we care to talk about at the present time,” Mara said. Does that mean that throughout the first season the building will be known as the New Meadowlands Stadium? “Not necessarily,” he said. So maybe something is cooking.