Because Governor and Lt. Governor are elected during the mid-term elections and not during the same election period as Presidential elections, it would be two years before Texans were given a chance to elect replacements. The job would then go to the Texas Senate to elect two of their own to fill the vacant positions. To do this, the Senate pro tempore (Sen. Mike Jackson) becomes de-facto Lt. Governor for up to thirty days to lead the Senate in its elections to fill the two positions.

So the question remains, who would the Texas Senate elect? Judging by the composition of the Senate, it would be two moderate Republicans that are respected in seniority. The two that immediately come to mind are Sen. Robert Duncan and Sen. Steve Ogden, both powerful moderates popular with the Senate leadership. With these two presiding over the legislature for the 2013 (83rd) legislative session, Texas would surely have an even less conservative session than the last.
While this scenario seems farfetched and obscure, it is definitely possible given the political atmosphere in the air right now. However, like the weather, political climates can change overnight and are very much subject to many interacting factors. It is too early to predict the climate in November 2012, especially because we do not know who the victors of the primaries will be or what large scale events will happen between now and then.