Yep. We said it. As far as parenting goes, this guy really blows at it.
Abe's dad, Thomas, is a weird mix of role model and anti-role model for Abe. For instance, Abe thinks his dad is lazy and not at all ambitious (1.23). That means that it's irony with a capital IRONY that Thomas's one attempt at ambition is what leads him to borrowing money from Jack Barts—which leads to his wife's death.
But before we even get to vampires, the first lesson that Abe learns is that he doesn't want to be like his dad. Which is why Abe is always doing, doing, doing, and everyone thinks he is hardworking. Just in case you didn't get that vibe when you read the book, here's some proof: "Gentry had come to admire the tall, hardworking, and modest Lincoln boy" (4.22) and "like most people who encountered Abe Lincoln, [Offutt]'d been impressed by the young man's hard work, intelligence, and general disposition" (5.34).
To make a long story short, Thomas is so lazy, so unambitious, that Abe wants to be nothing like the guy. He works so hard because his pops hardly works.
But Thomas isn't really the worst dad in the world, even though Abe doesn't exactly get along with him. For one thing, he was on the right side of history with his abolitionist views (you can thank his Baptist religion for that one), and Abe absorbs that political position from his papa, which tells us that Abe inherited at least one good thing from his old man (1.35).
Plus, Thomas Lincoln is one good storyteller. Abe tells us that, growing up, "Night upon night, I marveled at his power to hold listeners in rapt attention" (1.37). And as the narrator notes, Abe will get to be known as a great speaker and this will become a great help when he's giving political speeches. So did he learn this from his dad even though they didn't get along?
Probably. So maybe we should cut old Thomas some slack. He may not have been an awesome influence growing up, but he was an influence nonetheless. And hey, Abe turned out a-okay in our books. In everyone's books, really.