What happens if you can't - not because you aren't good at it, but because, well, you just can't.
Healthy and effective communication are dependent upon healthy and effective relationships. You can "communicate" until you're blue in the face - if you do not have the respect of the people you're addressing, it won't matter.
If you're a leader in particular, it's crucial to go out of your way to establish strong relationships with your subordinates, peers, and supervisors. I have an example of why I feel so strongly about this.
If you have a chilly relationship with a co-worker, where conversations are tense or cold or generally unpleasant, you will not communicate with them as often as you should. Consciously or sub-consciously, you will begin a futile effort of trying to anticipate their reactions to whatever you have to tell them, and because humans do that which is least painful, you'll avoid communicating with them until you get too far down the path (or worse, go in the wrong direction).
You may try overly hard to perfect whatever you're working on for your supervisor if you simply cannot get comfortable dealing with them, and what you end up with will have taken longer and not be as good as it could have been if you were working more closely - communicating more frequently and in smaller chunks.
Progress is impossible without collaboration; collaboration is impossible without communication; communication is impossible without relationships. People can have respect for leaders without liking them - that scenario may be fine in the military where collaboration is scarce or where matters of life-or-death put the importance of friendliness on the back burner, but it's a recipe for inefficiency and mediocrity in the enterprise.
If you're a leader, or you are subordinate to someone with whom you do not have a great relationship, do everyone a favor and make a renewed effort to get there.
People who have talent and respect for themselves do not want to work someplace where their efforts do not result in success. Talented people live for the chance to successfully meet challenges. If that's you, recognize the truth of this - you will never, ever get it done as well by yourself as you can with a team of people who share strong relationships. You owe it to yourself as a leader (by fiat, de facto or otherwise) to do whatever it takes to put differences or past issues aside, focus on the positives with everyone, and break down barriers to communication.