This won't take long. Obama said, if you like your insurance policy, you can keep it. Was that the entire story? Was he simply making a promise out of the blue?
No. He was not. He was responding to something. Remember what Republicans and Tea Partiers were saying, what they're in fact still saying: that Obamacare is something closer to what the British have, the single-payer, government-mandated system. They're saying it's a takeover, rather than a massive expansion of the private markets.
That put the reassurance in a different light: He wasn't telling people that Obamacare wouldn't put an end to some kinds of policies. He was telling people that Obamacare would not end the insurance system as we knew it, and that most people would keep their policies, because they were worried because of the lies that the Republicans were spreading. That right there is the critical point. Obama was responding to conservative lies about the Affordable Care Act, so the meaning of "keep your policy" changes dramatically.
I think the best response to these accusations is to present these circumstances, and then ask another question right back: why is Obama the only person being held to account for perceived dishonesty. These people talked about Death Panels, alleged a government takeover that was completely unlike what was actually there! Why are they not held accountable for their lies? At worst, what the President was only a little untrue. What the Republicans have been saying from day one has been fundamentally dishonest, and it's time to stop playing this game on the defensive.