Lord Stark storms through the castle like someone on a mission. A lackey tells him that there's a council meeting, but he has no time for that. He's looking for the king, you stupid lackey! Ah, but the lackey has the last laugh, because the king is the one who called the council meeting. Gotcha!
In the council meeting, Robert is displaying his usual tact and reticence by bellowing at the top of his lungs, "The whore is pregnant!" He wants to send some goons over to Vaes Dothrak to kill Daenerys and her unborn child. And "that fool Viserys as well." I love that even while Robert is freaking out at the prospect of a Targaryen coming back to challenge him for the throne, he's more worried about a baby than he is about Viserys. He has no time for Ned's complaints about honor, because honor doesn't keep the Seven Kingdoms in line. Ned says that killing Baby Targaryen would make them no better than the Mad King, which is not the sort of thing that Robert likes to hear. Varys says that his source is Jorah Mormont, who Stark immediately calls a traitor, and therefore untrustworthy. Littlefinger clarifies that Jorah was a slaver, not a traitor. Robert doesn't care about any of that and emphasizes that he doesn't want a male Targaryen at the head of a Dothraki army. He's all set to authorize some intercontinental assassination, but he wants his council to tell him it's okay. Everybody but Lord Stark is on board, so he tells them to get to work convincing Ned. Varys characterizes it as a vile thing, but one they must do. Pycelle asks how many innocents would die if the Dothraki were to invade, and describes it as not only wise, but kind. Renly thinks they should have killed the remaining Targaryens long ago. Littlefinger, if I have this right, says, "When you're in bed with an ugly woman... cut her throat." What? I may have missed part of his metaphor.
None of this convinces Ned, who decides that if everyone else gets to make a speech, he's damned if he's not going to get in a little oration himself. "The Robert I grew up with did not tremble at the thought of an unborn child." Robert is outraged at being defied, and he tells Ned to get with the program, "or I'll find me a Hand that will." Ned takes off the Hand's emblem. "Then good luck to him. I thought you were a better man." Uh oh. That's not the sort of thing that Robert likes to hear. As Stark walks out of the council meeting, Robert shouts after him, "Go! Run back to Winterfell! I'll have your head on a spike! I'll put it there myself! Shout, shout, shout." And so on.