Yes, there's been some back and forth here at the end, but as begging like this suggests, it's mainly been to sort out terms of surrender. His refusal defined the entire standoff.
That forced first Republicans and then House Republicans and finally the rump caucus of 50 to 80 House fire-breathers to stand alone with outrageous demands. By not engaging they destroyed themselves.
The 2011 crisis was, I believe, a turning point for Obama, not only because he realized he had been complicit in damaging the country but that his willingness to enter the discussion as a good faith, actual negotiation had the effect of legitimating what were actually rule-breaking, extra-constitutional demands.
It's far different, in many ways goes to the right-wing fever-dream fantasy Obama. But this classic scene does capture some of it.