Did any Senate Democrats vote against this? And if so did they supply a reason?
According to the vote record, there were three Democrats who voted against the nuclear option:
The rest of the Democrats and both independents voted for it. All the Republicans voted against it.
Chuck Schumer of New York may have argued against it, but he voted for it.
Levin gave a speech after voting against it. He specifically pointed out that once used, the nuclear option would eventually effectively change the rules so that they could be changed by a simple majority. He also cited specific instances when Democrats had used the filibuster to block Republican legislation that they found offensive.
I couldn't find anything from Manchin or Pryor from 2013. Manchin has talked more recently about it:
Well, I really don’t — I’ve been opposed to the nuclear option. I thought Harry Reid was absolutely dead wrong when he did it. And I voted against that. My dear beloved senator, prior to my coming here, was Robert C. Byrd. He’d be rolling over in his grave knowing what we have done and what we continue to do and how we really act out. So with that being said, I think it should be a bipartisan vote. I think it should be 60 votes for our Supreme Court. I think at the highest court of the land it should be what we are coming together as Americans and not to continue to divide us.
So he believes that the filibuster encourages bipartisan cooperation. He also feels that Robert Byrd would have opposed it. Byrd was a long time Democratic Senator from West Virginia.
Note that Levin has retired and Pryor lost his reelection bid. Manchin is the only Democratic Senator who voted against the rule change who remains in office.