When Arkansas jumped to the SEC in 1990 the final stage for the demise of the SWC was set in motion. The league had already been doomed by various factors, not the least of which was the unbridled cheating that had been rampant during the 1980's, but the Razorbacks defection sped up the process.
Back then Texas was ready to jump to the Pac-10. Again, outside factors stopped that idea in its tracks, and the retiring Pac-10 commissioner remembers it being a matter of Texas not being able to break away on its own.
Here is the gist of what Pac-10 Commissioner Tom Hansen remembers:
It's been a long time and memories do tricks to you but Texas was in my opinion based on communications, Texas was very interested and it thought initially might be able to come alone. Then about the time things were really getting serious it was made clear to us by Texas-Austin that it couldn't get clear of A&M. We invited A&M but before we got a clear signal from A&M, Ann Richards who was then the governor said Baylor's my alma mater and they're going wherever Texas and Texas A&M go and then in a less clear message, but still pretty well defined, we were told the legislators who control the oil money that goes to the Texas universities was controlled either by alumni of or representatives of the area of Texas Tech and now there was a group of four and we were not interested in going from 10 to 14 so we said 'thank you anyway.' But Texas alone was very favorably inclined to consider our offer.
Gov. Richards wasn't happy about the proposed move, but it was Lt. Gov. Bob Bullock who had the political will and the political power to make life miserable for Texas (and Texas A&M) should they decide to leave the SWC. Bullock, a graduate of both Texas Tech (undergrad) and Baylor (Law School), was adamant about the state university not leaving the others in the lurch. That along with other considerations, (travel, expenses, scheduling,) made the idea of Texas moving to the West Coast dead on arrival.
It wasn't long after that the the idea of forming some kind of alliance with the Big 8 began to take shape.