Obama is certainly playing his hand, no doubt about it. I think he's trying to use this situation to force Congress (both parties) to address long standing issues around both Social Security and Medicare. He's sees this issue as an opportunity to get something major done, since normally each party stymies the other. As a liberal, I'd rather see Obama address this issue than a Republican, because even if Obama does things I don't like, he won't be as bad as Republicans would be in my opinion.
Besides, the answer is quite complex, and there are different legitimate points of view cited in this article:
Can President Obama keep paying Social Security benefits even if the debt ceiling is reached? - The Fact Checker - The Washington Post
Late Tuesday night, however, the Treasury Department cast serious doubt on whether it was feasible to keep paying Social Security benefits if the debt limit had been breached.
“This type of financial engineering is untested, may not work, and is of questionable legality,” a Treasury official told us. “It is not feasible for Treasury to borrow from the public, each day, the precise amount of Social Security payments due without breaching the debt limit. In addition, it is questionable whether it is legal to redeem Social Security trust fund assets in advance of payments. Moreover, this presumes that Treasury will have full access to the financial markets if the debt limit is not raised.”