I'm not gonna hold too much fire to the Senate for not pushing that too hard. Keep in mind you can't get a President thrown out with just 51 votes. Do you really really think that enough Democrats would have come over to vote Clinton out of office? The Republicans knew that this was a lost cause in the Senate. I think it was good enough that they tagged Clinton with the Impeachment label.
Look at it this way. If by some reason they would have gotten Clinton out, or if he would have resigned, then Gore would have been President, and then Bush more than likely would not have been elected.