Will Tye just ran out of time.

If the Giants had gotten the ball back at the end of Saturday night's preseason loss to the Jets rather than allowing them to run out the final 7:31 of the game, or even forced a punt or special-teams play, Tye would have gotten into the game.

Instead, the tight end from Stony Brook University had to deal with the reality of suiting up for but not playing a single snap in what could have been his final chance to impress the Giants.

Now his time with the team may be running out too.

"It was definitely frustrating because that could be the last game [for me]," Tye said on Monday, the day before the Giants will trim their roster from 90 to 75 players, with further cuts to 53 coming on Saturday. "But I'll use that as motivation for this practice today."

It's an ominous sign when a healthy player does not see any reps in the third preseason game. Tye and third-string quarterback Ricky Stanzi were the only ones who didn't on Saturday. But others weren't far behind. Fellow Stony Brook University product Michael Bamiro, an offensive lineman, played only one snap on special teams and none on offense.

"My mind is just staying positive and being ready," Bamiro said. "I can't dwell on that. That would be shame on me. That would be my fault if I'm not ready for the next opportunity that comes at me. I'm just staying ready."

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That's not to say Bamiro isn't aware that he's on the precipice. He's just going to use it to his advantage.

"In the next couple of days, I'm going to show them exactly what I can really do on the field," he said. "Every chance that I get now on that field today and tomorrow is going to be way more physical and played faster than they've seen before."

Bamiro won't entertain the thought of a call from the front office, asking him to come in and bring his iPad in order to be cut. "I don't expect that," he said. "You have to stay positive."

Tye, though, said his mind has wandered there.

"I've thought about it, but not much," he said. "I feel like I have so much to offer, something will definitely have to come up. Even if it's not here . . . It's a business and things are going to happen not your way all the time. You have to keep positive. It motivates you and makes you want to do better."

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Unless there is some change in their course in the next few days, neither seems likely to become the first Stony Brook player to reach an NFL active roster. At least not this week. They could be picked up elsewhere or even land on the Giants' practice squad and await a possible promotion from there.

The good thing about that quest is that time likely isn't running out. And there aren't a lot of competitors, either.

"I definitely feel like I'm in the race for that," Tye said of aiming to be the first Seawolf to make it. "That's another good positive thing to think about."