I'm Jewish, and while I get intensely bored with all the Christmas everything creeping earlier and earlier into the year, I still love me a good Nutcracker. <3 I find that I vastly prefer being wished 'Merry Christmas,' as long as the intentions are good, over some form of combined 'Happy Chrismukkah!' mashup.
Getting on my seasonal soapbox: Hannukah has nothing to do with Christmas. It is not 'the Jewish Christmas,' nor is it 'Christmas, but, like, without Christ,' nor is it even a very important holiday as far as the Jewish calendar is concerned. It is a minor, non-biblical holiday, originally commemorated by eating fried foods and giving kids pocket money to gamble with. Presents were added in the 20th century as a reaction to mass-marketing of winter/Christmas as the season for giving.
Merging Hannukah with Christmas in pop culture does a lot more damage, imho, than acknowledging that our Christian friends and neighbours have a holiday that we don't, and enjoy wishing us the best.
Hannukah is a holiday to celebrate a successful guerrilla war / resistance against forced religious assimilation. Blending it with the majority winter holiday just because they fall around the same time of year is the ultimate in irony.
tl;dr: Jewish, and I don't mind. I'll wish 'same to you' right back, and all seems to be well.
(Now ask me what I want to say to the next little old granny on the bus who asks my kids about their lists for Santa, and then gets SUPER OFFENDED and argues with me when I say that we don't 'do' Santa. Because Santa is secular, don't'cha know, and Christmas is for EVERYONE... ARGH.)