I have no problem with Brits being furious at Obama. In fact, I encourage it. As long as it doesn’t lead to the usual America-bashing, of course.
It’s hard to tell how this will play out. Against all the odds (and all reason) Obama remains pretty popular in the UK. His intervention may very well encourage some to vote the way he wants. OTOH, I personally think its going to encourage many more people to vote the other way (and, unfortunately, encourage anti-American sentiment). No one likes to be bullied or threatened, and that’s what the subtext of his statement was. Not only that Britain was going to suffer for leaving the EU, but that America was going to punish us.