Byrd has been passed off by them as their "elder statesman" in the Senate, lending their party an appearance of dignity. He has a lot of seniority and all respect his expertise. It would pain them to have to trash him and, in the process, start fighting among themselves with a distinct risk of alienating their black caucus.
But even more important, they know Byrd would only be the first. They, above all others, understand that it's all about incrementalism and going for the throat. They can't let something like this avalanche. As I said, blacks are just beginning to look funny at the democrats, with Sharpton baiting them on practically a daily basis.