A very different President Obama showed up to tonight’s debate than the one who got trounced by Mitt Romney two weeks ago. Obama absolutely had to turn in a performance that would make his base happy — and he did that, by demonstrating a willingness to get in Mitt Romney’s face and in his space, and by not flinching from calling out Romney’s lies. Will Obama’s performance appeal to independents, swing, and undecided voters?

Yes, it will. The race will not be transformed in a fundamental way — it will still be a dead heat — but Obama accomplished something of a turnaround tonight. He took steps towards undoing the damaging dynamic Romney cemented during the last debate: One in which Romney had assumed the role of the energetic candidate of change, while relegating Obama to the role of listless, passive candidate of the unacceptable status quo — of the “new normal.”

I’d hoped to see Obama aggressively unmask Romney’s five point plan as a sham, as an economic bill of goods. Obama went some way towards doing that with a good line: “Governor Romney doesn’t have a five point plan. He has a one point plan.” That one point: Helping the rich get richer, so wealth trickles down to the rest of us. Obama repeatedly hit the theme that Romney would restore the same policies we’ve seen before. Romney struggled when a voter asked him how his policies are different from those of Bush. I thought Obama could have hit the ball harder at that moment, but he came up with an interesting argument, pointing out all the ways Romney is more extreme on social policy — the Blunt amendment and defunding Planned Parenthood — than Bush was. Obama’s framing of women’s health as an economic issue will surely resonate among the unmarried women he failed to connect with last time.

Obama drew a clearer distinction on taxes than he did in the first debate, which was absolutely critical: He repeatedly stressed that he would only raises taxes on the rich, while preserving the Bush tax cuts for everyone else. Crucially, he pinpointed this as a main point of disagreement with Romney, and didn’t let Romney get away with arguing that his plan would not cut the wealthy’s taxes. (It would, of course.) Even more important, he tied this dispute to a larger argument over economic philosophy, arguing that tax cuts for the rich don’t grow the economy, while tax hikes on the rich will allow us to keep up the investments in the middle class that will lead to lasting economic security.

And this is where Obama accomplished something really important: He got himself out of the box he’d blundered into during the first debate. As Dem pollster Stan Greenberg put it, Obama last time came across as the candidate of the not-good-enough status quo, rather than laying out a substantive second term change agenda of his own. By stressing his economic plan more directly than last time, by arguing that more jobs will be created in his second term, and by placing a heavy emphasis on our need to invest in alternative energy sources, he reoriented his argument towards the future, and framed it in a way that will appeal to independents and undecided voters.

Greenberg emails me that he is satisfied that Obama solved his earlier dilemma:

I thought he made the determination from the first second to be forward-looking — laying out each element of his economic plan. He repeatedly said, this is what I want to accomplish in a second term. While he clearly sounded confident about what he had done, he didn’t say, give me a second term because of a job well done. He repeatedly said , I would like another term to do this or that — on energy, education and others. I think voters will feel they heard him talking about the changes and progress he wants to achieve.

Ultimately, though, Obama managed the delicate balance of keeping his rhetorical fist in Romney’s face — challenging his evasions and contradictions and falsehoods — without coming across as overly aggressive, desperate, eager to make up lost ground, or unpresidential. As Taegan Goddard rightly notes, this provoked Romney, pushing him into a testy mode where he tried to roll over the moderator, which didn’t go too well.

This race will still be the dead heat tomorrow that it was yesterday, but Obama made big strides towards turning things around tonight.