SEE LATER POSTING FOR REVISED FIRST 13

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Damn!
Amadi saw the minutes fly off his watch as he thought about accepting the invitation out. Jessica was an attractive woman but clearly some time out with her would be hazardous to his health.
“I was thinking we could leave in about ten minutes, right after work.” Jessica’s smile calmed him for a moment.
Amadi glanced at his wrist again. He only had fifteen minutes left. Sweat began to bead on his forehead and his breathing quickened. That is the closest it’s ever been.
“I can’t. I have other plans.” The minutes rapidly increased, Amadi pulled his sleeve back over his arm. “And, I really don’t think you should go either.”

[This message has been edited by EVOC (edited March 15, 2011).]

The only thing I have to add is that I feel like there should be a more specific mention of "out." It just feels really vague to me, especially if he is saying "and I don't think you should go either." Does this mean that no one should leave work?

It is intriguing, but I think it is balancing on the line of too vague. It's not quite there yet, but make sure there is something more concrete coming up very soon.

Again, though, I think it has the makings of a good hook, just make sure it gets somewhere fast. Good luck

Damn!
Amadi saw the time fly off his watch as he thought about accepting the invitation out. Jessica had been all Amadi could think about since she was hired by the company. She was the most attractive woman in the office, but she had not even acknowledged Amadi’s existence. That is until now.
Amadi glanced at his wrist again. He now only had fifteen minutes left of life. Sweat began to bead on his forehead and his breathing quickened. That is the closest it’s ever been. Clearly a date with Jessica would be hazardous to his health.
“I can’t. I have other plans.” The watch froze, and then the minutes rapidly increased, Amadi pulled his sleeve back over his arm. “And, I really don’t think you should go either.”

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Damn!

This is catchy as a first paragraph, but it doesn't quite jibe with the contemplative nature of the followup. In the next sentence, he's thinking about a decision. Damn! might be better followed by something to more directly imply the intensity of the situation, like sweating or palpitations.

Amadi saw the time fly off his watch as he thought about accepting the invitation out.

Seeing things fly off a watch is a strange image. Would something like, "Amadi saw the seconds tick by on his watch..." be correct, or is the time flying off the watch important foreshadowing?

He now only had fifteen minutes left of life.

This is the crux statement, but I actually missed it on the first two reads. It's dropped in after glancing at his wrist. Can this be accentuated somehow, like "... again: fifteen minutes left to live."? Also, his action in paragraph two is looking at his wristwatch; if he glances at it again it's implied that he does something else in between, like pacing or shutting his eyes or staring into space.

That is the closest it's ever been.

Present tense, unlike the rest. Is this a thought? "That's the closest it's ever been, he thought."

The watch froze, and then the minutes rapidly increased, Amadi pulled his sleeve back over his arm.

Comma splice after "increased." Maybe "and" before "Amadi" or turn it to a period or a semicolon.

These are nitpicks; I like the concept. Send it if you'd like a reader.

Edited: Because I screwed up my punctuation after nitpicking about punctuation.