Final answer:
The false statement regarding Texas Governor's powers is that the Governor can only veto bills while the legislature is in session. Governors have the power to veto post-session and to call unlimited special sessions, controlling their duration and agenda.
Step-by-step explanation:
The statement that is NOT true regarding the Texas Governor's powers is: 'The Texas Governor can only veto a bill if the Texas Legislature is still in session.' In fact, the governor has the ability to veto legislation even after the legislature has adjourned, similar to a president's pocket veto at the federal level.
Texas Governors possess considerable power over legislation. They can veto any bill or specific items in appropriation bills, and while the Legislature can override a veto by a two-thirds vote, this requires significant agreement among legislators, which is often challenging to attain. Moreover, special sessions are a strategic tool for the governor, who has the power to call the Legislature into these sessions and designate their agenda. Although each special session is limited to 30 days, there is no limit to the number of special sessions a governor can call.