Was Charles Whitman having mental health problems? Did what guns he used matter? Was he a Democrat?
This picture is mostly true, but leaves a lot of important details out, and while it makes the point of the problem, fails to grasp it.
In addition to the Remington 700 mentioned in this graphic, he also had a .30 caliber M1 carbine, a sawed off semi-automatic 12 gauge shotgun, a .35 caliber Remington, a 9mm Luger pistol, a Galesi-Brescia .25-caliber pistol and a Smith & Wesson M19 .357 Magnum revolver, 700 rounds of ammunition and several 15 and 30 round clips. 
He was a Marine, a highly skilled marksman, and had a 172 IQ. He was court martialed for illegal possession of a firearm on base, and threatening other marines. He was also addicted amphetamines and was having health issues including severe headaches. He had been to the doctor’s office requesting psychiatric help, saying he had feeling of overwhelming violent impulses and had requested that an autopsy be performed after his death to determine if he had any visible physical disorder (he had a fatal brain tumor). In his last note he requested that any life insurance money be donated to a mental health foundation to prevent further tragedies of this type. If his doctor could have warned police that might have helped. 
I have found absolutely zero evidence corroborating that “fact” that he was a democrat, all biographies, stories, his own journals, and books written about him fail to mention his voter registration, who he voted for, or any political ideology whatsoever. If you have found different, please submit it.
These are perfect examples of why not allowing people with mental health problems to own guns, or taking away guns from people who are obviously a danger to themselves or others would be more help than gun bans. Gun bans wouldn’t have helped, gun magazine size bans wouldn’t have helped, what type of guns they had wouldn’t have made a difference. Off the top of my head, in recent shootings, the Aurora shooter, the Newtown shooter, and the Virg. Tech shooter all were seeing psychiatrists for mental problems. They would have more likely been stopped by a call to the local police dept or never having been able to buy those guns (or have access to them) than a gun ban.