I noticed years ago that our culture is more inclined to formality where men are concerned, and presumptively informal with women. (And just generally inclined toward overfamiliarity in general, but that's another issue.) Very few people speak of "George"; even his detractors prefer to denigrate him as "Dubya" or "Shrub." No one has referred to Republican candidates as John, Mitt, Mike, Ron or anything else, nor have we referred to John or Barack. I don't see a particular reason to refer to the senator as Hillary either.
Why? Because it's more respectful, more formal, and more befitting the relationship we have with her. The Clintons are not close and personal friends of ours, they are not likely to come over to our houses for a cup of tea, and, when you get down to it, our chances of meeting them hover somewhere slightly above zero.
Sen. Clinton may be using her first name for a variety of reasons: to differentiate herself from her husband, to create the feeling of intimacy and familiarity with voters, or because it conjures more pleasant associations for her than the name of a small township in New Jersey off Route 78.
I don't believe anyone here has been uncertain who was being referred to when we use the name "Clinton"; and as has been pointed out, there are plenty of ways to make the distinction should confusion arise: Sen. Clinton and President Clinton, Mr. Clinton and Mrs. Clinton, former President Clinton and President-elect Clinton, and so on.
I think it's better to show Clinton the same formal respect that we show to her opponents and her other peers.