The team decided to cut a branch of the code that I have been tracking. After they did that, I ran git svn fetch. After doing this, Git realized that a new branch was created and it started to search through the subversion repository to pull back any history that it might not have.
This probably is a good idea, if I were tracking the entire Subversion history, but I am not. The result was Git was starting to pull back history that I didn't have in my Git repo, nor history that I wanted. It would have taken hours to pull in that amount of history, and as I mentioned, I was not interested in retaining the whole entire repository.
In order to resolve this, I performed the following command:
git svn fetch -r
I think that the most important part of this command is the --no-follow-parent. This tells git not to look back in time at the history, and just pull in the information from the specified starting point.
I hope that this helps someone else out there....
Pay it forward.