How should we deal with our toddler's verbal threats of aggression against our new baby?

First, look at the positive side of this. Your toddler is verbal enough to express his frustrations about this interloper. He's using his words, not his fists, to tell you how upset he is that this baby has arrived on the scene and interrupted a perfectly good situation he had going.

At this point, you should supervise all their interactions. Impulse control isn't high on the list for toddlers, so you don't want to let him do anything he (and you) will regret.

Encourage your toddler to talk about his feelings. Acknowledge that it is hard when there's a new baby in the house. Infants take up a lot of time, receive an inordinate amount of attention and aren't much fun for an older sibling (at least, not when they're tiny). If you can, tell your toddler about how you felt when your younger sibling was born (or recount other family stories you've heard). This will reassure him that he's not alone in these emotions.

Carve out some one-on-one time for your toddler. He needs to know that he's still got his place in the family even with the newcomer's arrival.

Right now your toddler may not realize it, but a sibling is a wonderful gift to give a child.