I hate watching Texas lose too, but I believe that changing coaches on a whim is not the answer. You'd say that 3 years is enough time to fix the problem, but it really isn't.
First off, changing coaches brings change, but at a slower pace. Read this NYT Article and you'll find out why. It has taken three years mainly because:
Year 1: Old coordinators.
Year 2: New coordinators.
Year 3: Young Team (losses on defense from last year).
Now, what about year four:
An experienced team (most sophomores). Experienced offensive and defensive staff.
Mack Brown certainly deserves another year. If next year, Texas does not make it to the BCS, then Mack Brown should realize that someone else can do a better job, and resign with his head held high.
This is the logical way to go. All those who are asking for Mack's head are doing so out of emotion and not really thinking rationally.