Realistically speaking, no. Such a thing would cause too much of an uproar from the Christian base who don't realize that it wasn't originally a Pagan holiday/etc.
Ergo, as Shanghai Alice said, "If it ain't broke, don't fix it."
I've always felt a special bond to Christmas [as it is the day of my birth and whatnot], and I don't see the point of changing it at this point. While the origins of the holiday are not exactly ideal [Pagan / Jesus's birth likely being in summer ], it was decided that December 25th would be designated as the celebration of his birth. So, for Christians, it can still be a celebration of his birth, even if it's not on his birth day. It's just something everyone agreed upon, and to change it would be utterly pointless.
Furthermore, to completely disassociate religion with it is completely and utterly absurd, and just wrong. If people want to celebrate their savior's birth along with everything else associated with the holiday, so be it. You have no right whatsoever to force your beliefs upon them.
However, I am still for saying Happy Holidays, as I believe it's the most absolute neutral way to express the passing of love of the season [as stated, there are several other holidays that are celebrated around this time, or people don't even celebrate at all].