I suspect that President Obama's legacy won't be the renewal of NATO, but the recognition that during his term everyone else realized that NATO is not obsolete and set the stage for others to renew NATO.
I haven't been in the "NATO is obsolete camp." NATO (with a strong American presence) is a bargain form of insurance as far as I'm concerned.
I think my decade-old article on the Army in Europe is as good a place to start as any, although my view of Russia's threat was clearly in the "just in case" category of worries as part of hedging against future unknowns.
The arc of crisis that Army units in Europe can react to now extends from northern AFRICOM into CENTCOM and then north of the Greater Middle East into EUCOM all the way up to the North Pole, I think.
So yeah, I think the value of NATO has been recognized again. But I sincerely doubt that President Obama will take the lead in revitalizing NATO.