In a word, yes. Or at least we have to try.
There is a glimpse of hope, according to the Guardian:
BBC Trust chairman Sir Michael Lyons said that if there was a big enough public response about the cuts, he would ask management to rethink its strategy."If we find that... there's massive public concern that we need to take account of then we will go back to the director general to rethink the strategy before it's approved"
So if you're a listener, please email them: trust.enquiries@bbc.co.uk UPDATE: and also: srconsultation@bbc.co.uk
(If you need inspiration this open letter by Jon Ronson should help...)
Or take part in their online consultation on the cuts,or what they are calling a "strategic review" (and this will probably have an even better effect because it's what they are officially asking you to do).
UPDATE: Also join the Facebook group and sign the petition and keep up to date with the latest news more info at: http://www.love6music.com

I agree with Stu that 6Music is the only station worth listening to. Of course axing the Asian Network also seems, as Billy mentions in a comment over on Under the Radar, to be an ominous sign when it comes to the BBC's supposed public service remit. But I won't pretend that I was a listener or expert on that particular station - and there are mixed reports of how high regard it was held in by even the Asian community itself.
Of course, as a number of commentators have already pointed out, 6Music is far from perfect. It has some deep flaws, such as a propensity to play the same songs too often during the daytime, e.g. I like the latest single by Hot Chip but do I need to hear it 100 times? Steve Lamacq has the most tedious chat and musical taste outside of a Razorlight concert and clearly lives in a fantasy world where br*tp*p is still relevant.
An infuriatingly repetitive and patronising music news slot which features the pointless and smug Menswear drummer peddling management approved faux-credible crap like Ellie Goulding (whose success was apparently pre-determined by a record company memo while she was still in the womb) is another way that the head honchos have misinterpreted what the station's audience is actually there for, as Mogwai's Stuart Braithwaite commented on Twitter in his uniquely eloquent way.
The decisions of Lesley Douglas, as
Stuart McHugh (one of Scotland's most clued up and consistent supporters of new music) points out, are central to the problems the station currently faces. Because she was also in control of BBC Radio 2, she effectively neutered 6Music by making presenters interchangeable. By moving presenters between stations regardless of musical taste, she destroyed any brand differentiation between the stations and paved the way for Russell Brand's and her own demise.
After all if the misjudged Brand/Wossy phonecall had have happened on 6Music where Brand's show began and should have stayed, it may not have created so much anger (as most of the furore was over such a thing happening on the national institution that is Radio2) or even happened at all. Of course she had to resign over that instead of what she should have been roundly caned for, her widely derided decision to employ the hollering mockney George Lamb.
The main disadvantage that 6Music has had though, is that most people hadn't heard of it. Whilst the uproar about its closure will certainly do something to increase the number of listeners, with even the idiotic
Tory Culture spokesman being a new convert, the problem is mainly that it can only be listened to on a DAB radio. It is literally the only station we use our DAB radio for, and if it is closed it's hard to see why having a DAB radio is necessary at all. In fact, I would say the vast majority of people in the UK who own a DAB radio bought it solely to listen to 6Music. If it was on FM things might be different. If it was publicised properly by the BBC things might be different.
So as well as emailing or filling out the online consultation, how about letting people you know that the station exists, and probably caters brilliantly for at least one of their musical preferences. If they like funk and soul, direct them to Craig Charles excellent Funk & Soul show on Saturday evenings. If they like avant garde and weird crazy music, tell them about the Freak Show. And if they like to hear some of the latest decent music, including the really good stuff from Scotland, and want the closest thing to John Peel, tell them to tune into Marc Riley on weekday evenings. Hell, then there's Jarvis Cocker, Guy Garvey, Gideon Coe, Lauren Laverne, and of course the chance that, if we could just save the station, Adam & Joe could come back with their incredible Saturday morning programme.
Of course all the optimism in the world might not save the station, but it's definitely worth a try - and now is the time, before it really is too late and both musicians, music fans and DJs alike will all be much worse off.
Here's some hope. A lot of people have wondered aloud why the devastatingly patronising and cheap BBC3, (which recently brought us a programme where a mother competes with her daughter to be judged as 'hotter') was not axed instead of these more worthy radio stations. As
Vicky Frost at the Guardian points out, the channel's bosses can point to successes like Gavin and Stacey (which frankly I never understood the fuss about) and Being Human as the reason for it to survive. Well Being Human is indeed a brilliant programme, and the only reason it ever got past the pilot was because of a public appeal by viewers - they were going to commission the pish-poor Phoo Action instead (again, that was for political reasons - because it was shot in Scotland and they needed to be seen to be funding programmes made north of the Border).