Haven't been able to find this on the wiki.

Will they turn you down the MOMENT you have any negative rep, do you need more positive than negative rep or what? Got the embassy pardon if I need to use it, but I'd rather not use it for the sake of getting the right Lonesome Road dialog.

You need more than neutral, my current playthrough I'm trying to be hostile with the NCR and while they're not hostile with me, yet even though I eradicated Forlorn Hope and shot a few randon NCR mooks here and there, I wasn't able to complete the quest to save the pres from his own stupidity due to my low rep.

I wish the rep descriptions were more intuitive. What does soft hearted devil mean???

You definitely have to be in good standing with the NCR to help protect the president. I mean, of course they wouldn't accept your help to guard the highest member of the NCR, if they can't trust you. So, negative rep is a definite no-no.

@ Primm: Soft hearted Devil means you are more infamous than famous. http://fallout.wikia.com/wiki/Fallout:_New_Vegas_reputations