The substance here is silly but the implications are serious. These cuts have happened, they've been passed into law, and so there's no real reason to be arguing about them. But whether they're counted in the budget deal is important in terms of deciding the abstract ratio of spending cuts-to-tax increases.
Imagine that Boehner and Obama end with a deal that includes $1 trillion in new spending cuts and $1 trillion in new tax increases. If the BCA cuts are included, that's a 2:1 deal (and it becomes a 3:1 deal if you include the drawdown of the wars in Iraq and Afghanistan as spending cuts, as you almost certainly should, but let's leave that out for the moment). If the BCA cuts aren't included, it's a 1:1 deal. And Boehner can argue that it will be very hard to sell his members on a 1:1 deal.
Note that though the politics of these two scenarios are very different, the policy is identical. Ever heard the saying "that's a distinction without a difference?" This is a not-distinction that makes a big difference.
And here it is in graph form:
This is, to my mind, a much clearer way of thinking about it: The "grand bargain" involves a couple of categories of policy, and the "discretionary spending" category is finished. You can either include that in the ratio of throw out the idea of a tax-to-spending ratio altogether, but you can't pretend the BCA cuts didn't happen.