Politicians are often put into difficult spots. They are damned if they do, and damned if they don’t. Regardless of what they say, someone is not going to like it.
The Obama example you gave is actually, in my opinion, a great response to that difficult situation. Political yes, but it helped him stay elected. Just because you didn’t like it does not mean he should be impeached.
I spent six years a party politics. I saw the compromises politicians have to make as they navigate tricky waters. I could not do better. Neither could you.