I think part of the trick to keeping it straight is to focus on the presser foot and the edge of the card, not on the needle. Try practising with some scrap paper so you get the feel for how fast you can go and what the "pull" of the machine feels like as you control the paper being fed through, keeping your eye on the edge of the presser foot all the time.
The other trick is to make your stitching deliberately wonky! This can be a really nice look and it frees you up from worrying about it. Go round two or even three times and let the lines overlap for the best effect. I've attached a sample so you can see what I mean.