MBaller.
I used to have the same problem. It took me a long time to figure it out. What I did was to not copy the original phrasing of the song I was covering but started to switch it so that it was more comfortable and natural feeling for me. I just experimented a lot and did it A LOT! Also of importance was doing my own songs. I would take cereal boxes, letters to chicks, newspaper articles or whatever and then sing them to what ever rhythm I came up with. It made it hard to get it wrong that way and it gave me confidence that I could get a groove going and not stumble trying to cop someone else's phrasing.
Another thing I did was to put down the guitar and get a metronome and/or drum machine and start singing to the beat. I would try singing the same phrase ahead of the beat a little bit (rush it), on top of the beat (dead on), and behind the beat (drag). Just experiment but do it untill your eyes pop out or you turn 40 years old. Then you'll have it for sure. If you are already 40 then, hmmmm.......
All this time you should be getting rhythym really programed into your picking/strumming hand so that you can't loose the beat no matter what. Try thumping on what ever you can find with your hands during the times that you can't play guitar. Whatever you can think to do to become a HUMAN RHYTHM MACHINE! Then it's easy.....well, some of the time ;-)