The backfire effect is a one-way door for conservative disinformation. The short version is that Romney's lies will stick better if the President tries to deny them.
It doesn't work the same way with people who can actually think, so it only works for Republicans and against Democrats.
What I think this means is that Romney will be encouraged to lie even more than usual, if possible, and the President will have to address those untruths in some oblique, complicated way which turns the problem on itself and makes conservative voters doubt their pick.
That seems to require an assertive approach, as you suggest, and probably also the President will have to memorize hundreds of Romney's prior lies and position-shifts so that he can retort by quoting Romney against himself.
As a former legislative analyst, I can say this: nobody is or has ever been better at taking Republican flaws in character and ideology and forcing the GOP to damage themselves with them. If anyone can find a way around the backfire effect, it will be President Obama.