Make the 1968 Democratic National Convention, which was swarming with anti war riots IOTL, as troublesome and destructive as possible. Could it have been so bad, that the violence spread into other cities? How long until LBJ can subdue the rioters?
Remember IOTL Mayor Daley had requisitioned Illinois National Guard from his tool in Springfield, Otto Kerner. What would the POD be? If Humphrey outright called for the full prosecution of the war, that could cause more disturbances. Another one could be LBJ walking in and taking the nomination on the floor. He considered this but never found an opportune moment. When the polling commissioned showed him doing worse than HHH IOTL and losing the entire South to Nixon/Wallace except TX, he decided not to. Also the fact that now RFK was murdered, this would be "feasible". Don't underestimate LBJ's callousness on this point. He wouldn't sign the appropriation for an Arlington grave, leaving it to Nixon, who acted quite decently (Kennedy and Nixon if you're interested) in this regard. That would cause a huge explosion and a 747 load of hate mail to the WH. But LBJ didn't give a damn.