He refused it, because he believed that it's an act of treason and didn't wanted to accept it as a governor. Because he was removed from his office. He decided to move himself away from politics and died on the country side in 1863.
Explanation:
Sam Houston, one of the most famous historical figures in 19th Century refused the secession, but furthermore refused to help Union in fighting the Confederates. He didn't wanted to participate in the bloodshed, as he was someone who fought for the unification of States, not its dissolution.
The Depression affected politics by shaking confidence in unfettered capitalism. That type of laissez-faire economics is what President Herbert Hoover advocated, and it had failed. As a result, people voted for President Franklin D. Roosevelt (FDR).