As a general point, I think "making people take semi-embarrassing votes" is vastly overrated in American politics. Can anyone think of a campaign that even partly turned on one of these gambits?And so does Jonathan Bernstein, who quotes Klien approvingly.
I will admit that my response on this answer may be tainted by my time on campaigns and my years away from the academic study of Political Science. But I actually agree with Kevin Drum and I think that Ezra and Jonathan are taking too narrow of a look at the issue. It's not about a single, individual campaign wherein one vote on repeal is going to tip the scales. It's about creating a narrative of Republican's kowtowing to big business, seeking to deny benefits to average American's and the general insanity of the Republican Party. A vote in the Senate on health care repeal would garner significant media attention and begin to create that narrative.
Now if there is any data points out there that will rebut my supposition I have no doubt that Bernstein will provide them. And I'm open to persuasion on this but, for now at least, my gut says hold the vote.