A few thoughts on these 2 appointments:
First, two cheers for Cecilia Rouse! She's an education economist and much of her work documents how school choice programs improve educational outcomes for poor and minority students - especially when it comes to math. She also documents positive outcomes from performance incentives for schools. To be clear, I don't doubt she's a liberal and that she and I likely differ on many issues. But this particular question has been one of the main issues on which her research focuses. I wonder if any of the Democratic Party's teachers union allies will oppose her appointment (though the Council of Economic Advisers has only very modest policy influence, of course). Hopefully they won't (perhaps because they won't want to be seen as blocking an African-American woman).
Tanden strikes me as a smart and capable person who just simply doesn't know much about the constitutional issues involving constitutional challenges to Obamacare. The AHIP event should have been a favorable audience for her, because insurers liked a policy that required people to buy their products (or at least pay a "tax" if they chose not to, if you buy the Supreme Court's ultimate interpretation of the law). But Tanden didn't do too well, because she just wasn't prepared on the issues in question.
I don't have a strong view of whether Tanden should be confirmed or not. But, on balance, I would probably prefer someone who knows more about the issues, and is less inclined to "wing it" than she seemed to be. But I readily concede she might be better on other issues. I would also prefer an economist type at OMB over a liberal policy activist. Tanden is clearly the latter. I often find lots of common ground with people on the left who are familiar with Econ 101 and rigorously apply it to policy issues, but have many more divergences with those who aren't and/or don't.
There is a good chance Tanden will be rejected by the Senate. Not because of the matters that bother me, but because she has said a lot of harsh things about various GOP senators, including key swing voters like Susan Collins. Personally, I don't care much about that. The senators themselves are likely to be less forgiving, as some of them have already said.