Obama can hit back without compromising his promise of a new kind of politics by focusing on these three things: Character, electability & Identity.
1. Character: HRC wants to count the votes in Michigan even though Obama was not even on the ballot. This speaks to her character. He should not be afraid to highlight this and distinguish himself as someone who would not do that, even if it was advantageous to his campaign. She is willing to undermine Democratic chances in November to advance her own campaign. These differences are stark. He's better than her and he should say it.
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2. Electability: Every right wing talking head I've ever heard of is on video saying she's the one they want to run against, she'll unite their party, she'll activate their base etc. That's a fact. It's okay to say it. Democrats need to understand that (it's a miracle all the HRC supporters don't). The next TV spot should be a montage of everyone from Ari Fleischer to Joe Scarborough saying Hillary will be the easier target.
3. Identity: Too many people don't really know who he is. He needs to give a speach like, and I can't believe I'm saying this, Mitt Romney did. We all know his bio well, but it's clear a large part of the electorate do not understand his story and they're not about to read his first book. He needs to talk about his Church, why he became a Christian, what he really believes in. This can't be ignored and must be addressed head on in his best format; the speach.
Further, he needs to talk about who she is. No one could have walked into the state of New York in 2000, having never lived there, and get elected senator if they weren't married to the president. That's not an attack, that's a fact. While she's very talented and highly intelligent, she owes her current position to the fact that she was married to Bill.
Everything Obama has and everything he is is the result of his own hard work, talent and intelligence. He's self made in every way, the true American story. HRC is trading off of her name.