Jenelle Evans' Husband David Eason Could Face Jail Over Child Support

David Eason doesn't just abuse and kill helpless animals -- he's also allegedly abused his baby mama and fell way behind on child support payments ... and if he hasn't paid by today he could end up in jail.

Eason is currently under criminal investigation for animal cruelty. As we reported, earlier this week he savagely beat and then shot his French Bulldog which barely nipped at his 2-year-old daughter's face. The nip was so minor it didn't draw blood or even puncture the skin. We're told David repeatedly slammed the dog on the back porch before taking it to the backyard and killing it with a shotgun.

But, his troubles don't end there. Eason briefly dated a woman named Olivia Leedham in 2013 and the two had a son together. Leedham went to court, claiming Eason shoved her when she was 8 months pregnant and left her in the middle of the road at night when she was 7 months pregnant.

The two have been in a nasty custody battle for years ... and we've learned he's fallen thousands of dollars behind in child support. His deadline for paying it is today, and if he hasn't anted up he could end up in jail.

Animal Control officers were unable to talk with Eason during their visit Thursday because the family's pit bull was on his front porch and "No Trespassing" signs were posted on the property. Animal Control officers didn't feel it was safe to enter so they asked the Sheriff's Department to figure out the next move.