How many times has the US Senate had
more Senators go one way and
more population represented want the other way?

You can figure out how many people a Senate vote is representing pretty easily by counting the population for the state of each Senator. If 55 Senators vote one way but the other 45 Senators represent more people, I think something is fishy. Let's call such an event an inversion. I analyzed the Senate voting record and estimated population of the states from 2000 to 2009 and came up with the following:

That this is possible should cause doubts about whether the Senate is the best possible form of that part of our government. That this is in some years quite frequent should make us seriously consider reforming the Senate.

It won't be easy. It might require an amendment with unanimous ratification. It might require a new constitution ratified by a new constitutional convention of the States. Right now I just want more people to agree:

The Senate is undemocratic.
It is a problem.
We should fix it.
rant:

The Senate is obsolete. It may have been a good compromise in 1783 when the States had some real potential to give up on their loose confederation and just all be their own little nation-states. I don't think that has been relevant for well over a hundred years. Most people now alive don't know the United States of America is anything other than United. The States don't have any meaning outside of the United States. They are a convenient traditional subdivision of government, but they do not specifically need to be represented at the national level. I think Democracy should be about people voting, not lines on the map voting. One of the great features about our Constitution is that it recognizes we might need to change it sometimes. I think we should change this.