From the Handbook of Texas:
But when he refused to take the oath of loyalty to the newly formed Confederate States of America, the Texas convention removed him from office on March 16 and replaced him with Lieutenant Governor Edward Clark two days later. Reportedly, during these traumatic days President Lincoln twice offered Houston the use of federal troops to keep him in office and Texas in the Union, offers that Houston declined, again to avoid making Texas a scene of violence.
p.s. My Uncle Sam was a delegate to the Secession Convention who voted to give Gov. Houston the boot. The signature of Sam A. Willson is the last one.