Maybe you did not know this, but overall, every President since Reagan has followed the basic plan to decomission our (America's) nuclear arsenal, not to mention our chemical and biological arsenal (which has been actually destroyed and not just decomissioned).
So, what Obama is saying is almost exactly what the past 3 presidents have said (Bush Jr. did start-up a new nuclear program in 2003, under the guise of helping the war on terror, but they have been unable to accomplish anything of importance outside of the negative factor of forcing Russia to revamp their program). There used to be around 65-70,000 warheads, now there are only 20,000, so literally every country that posses a significant stockpile has helped in the decomission process. (That being said, since Russia is not an actual enemy anymore, it has been statistically shown that as few as 200 nuclear weapons are all that is needed to act as a deterent against significant foreign threats, the only reason we still have so many nuclear boms is because Russia has taken significantly longer to decomission their arsenal.)
As to the comments of the QDR; the system needs drastic reform, specifically due to the fact that a majority of the review is structured to deliver a response to a threat the size of Russia, not the size of Iraq (the QDR literally is stuck in the Cold War). So, an oversight committee is needed to cut out large sections of the review, and save the taxpayers upwards of a 100 Billion dollars (that figure is probably exaggerated by about 50 Billion).
That being said, Rumsfeld, in his original 2001 QDR, proposed almost every single thing that Obama has proposed, but due to 9/11 he drastically changed his response, instead foolishly keeping the old system in place, when it needed drastic change, and not budgeting sufficiently for new technology or innovatioin, and then in 2006, he blew it again (raping the budget this time) and simply let the commisioned officers at the Pentagon waste money on equipment that was un-needed for the current style of warfare (why do we need more F-22s, new nuclear-subs, and a new aircraft carrier, let alone dozens of other expensive yet fundamentally useless pieces of equipment in the "war on terror").