There's a good article here here about liberal opposition to common core, worthwhile not least because of its own links. Common core is currently best known as a bete noire of the right, including politicians like Bobby Jindal who were all for it until five minutes ago. Arne Duncan, CC proponent and the current Education Secretary, is certainly a deserving target, put there by Obama. Hillary Clinton, from everything we know about the Clintons' associations, would almost certainly have appointed Duncan or someone indistinguishable as well. And a Republican presidnet might have given us a Secretary Michelle Rhee, a hair-raising prospect. So it's not really a partisan issue, and a non-depressing political outcome is unlikely in the short term. There needs to be grassroots resistance, which luckily has started to arrive.
My own opposition is rooted in the time I spent taking the preliminary classes for teacher education back in the nineties. While I didn't go on to the profession myself, I got to know a lot of other people who were preparing to become teachers. They were a varied group, some very inspiring, some very much not. But the best, it seemed to me, were the ones who best knew their own rhythms, and thus would be most resistant to rules set down by a far-away technocrat. I have friends who do teach now, and I think time has borne me out.