Senator Eltife’s proposal to apply Executive Officers to a limit of two term was passed in the State Senate today. By a vote of 27 (15 Republicans, 12 Democrats) to 4 (all Republicans), the State Senate moved the proposed Constitutional Amendment to the House. If it passes by at least 2/3 majority in the House. The Chron article mentions that the proposed amendment exempts current officeholders, meaning Rick Perry could stay in office until 2023.
You can see my thoughts on term limits here. Essentially, I support this proposal, because it only applies to Executive Officeholders. I support term limits on the Governor for the same reason I support them on the President: it prevents too much power being concentrated in one person for too long. I find it pretty interesting that comments on the Chronicle are so supportive of this measure (albeit, opposed to the fact that the term limits exempt the legislature), I had always figured the internet commentators there to be more libertarian than that.