It was time, the draft had been sent out to all the men across the nation.
I think a full stop after 'time' would make this more urgent. I wonder, too, about 'men'. What age is the draft - over 16? I get the impression that a lot of draftees are still just kids - maybe there's a better and more effective word than just 'men', which is quite a dull word (in this context *cough*

)
It could be heard everywhere, loved ones crying for those who may never return from the war, who may never actually come back in one piece.
Semi-colon after 'everywhere' - or separate the sentences.
'actually' is a horrible word that should be banned from both written and spoken English. It actually doesn't fit in anywhere

Everyone knew that it had been coming for quite some time, it just came at the worst time of year, it was no more then a week before Christmas, the families were settling down, many had thought their government would give them that much, but they were wrong.
I'm quickly using up fingers counting how many times you've used the word 'time'. The repetition is cumbersome. You need to separate your sentences into sentences, too. Commas are incorrect when used instead of full stops.
"But do you have to baby?" The question was thrown from a new mother of a month old child, the large blue eyes looking up to the love of her life. The 6 foot man wrapped his arms about the 5'4 woman, a small kiss planted on the top of her head.
"But do you have to, Baby?" Comma and capital letter, otherwise 'baby' is a verb - as in 'to baby your little sister' ...
I don't get the six-foot and 5'4 - perhaps one or the other, but telling us the height (very uninteresting detail) of your characters does nothing to endear them to us. Tell me something that might make me want to care whether he leaves or not. Her height is really irrelevant.
The man just rocked her back and forth in a slow loving manner, murmuring quietly into her ears trying to reassure her.
Don't overwrite. 'In a slow, loving manner' is superfluous here - he's not going to rock her violently or, if he is, then the adverb 'violently' would be acceptable because it's unexpected. Does that make sense? Same with 'murmur quietly'. Take out 'quietly' because you can't murmur any other way.
There was a 3 day notice, and the two of them spent all three days together,
This is really an editing point, but might save you trouble later. When it comes to numbers/names, etc. decide how you're going to write them and be consistent throughout your story - so if you're going to use numbers, use them. If you're going to spell numbers (usually, we spell them out up to ten and then start using figures) then do that - but don't use variations. It's simply a pain to correct later on and makes it easier if you do it from the beginning.
unable to leave the others sides, but finally the fateful day came. He got into that black mustang that was sitting in their driveway, exiting in reverse, and slowly driving off towards the military base where they were to be transported away to Vietnam.
Mixed-up tenses here. I think you mean 'exited' and 'drove' (avoid 'ing' when you can - at any point in your writing)
His hand reached into his pocket a few times on his long drive, and after the 5'th time he noticed a small slip of paper.
It's a personal thing, but I always have a probably with limbs that act of their own accord - and there isn't a reason for it here anyway. Why did he (not his hand

) reach into his pocket? Maybe he had some sweets in there? Or he'd stolen his new daughter's dummy as something he could keep with him??? Give it a reason.
Definitely 'fifth', not 5th
Pulling over to the side for a second, he stopped opening the paper delicately, and took in the words that were written upon it. 'Don't forget to write baby.' The red lips slowly curved a bit at the corners as he looked at it. "I won't honey."
Comma after stopped - otherwise it's exactly the opposite of what you want him to do (i.e. you don't want him to stop opening the paper, do you?

)
Red lips? Is he wearing lipstick? That's what it sounds like.
Quick punctuation point which will save work later ... before you address somebody - by name, nickname or whatever - you always put a comma and then use a capital letter, so ...
Don't forget to write, Baby
I won't, Honey
Otherwise, 'baby' and 'honey' are simply two verbs and they don't make much sense.
Good start to this story. It gets straight to the action and immediately introduces us to a main character without any messing around so this is great. Remember that the simplest writing is always the best and the most effective so be careful with overwriting. I'm looking forward to the next part when I can get around to it. I'm intrigued by this character because he's off to war and gives a bit of a touch image (even though he's been drafted) but this is nicely offset by a soft side as he reads the letter.
Good luck. Hope this helps and isn't too harsh? It's not meant to be.
Symphony