Actually, Obama has directly linked Social Security to the deficit

You stated:
Still, it's unlikely that the President has cuts to benefits in mind because he has always stressed that he will protect benefits and that Social Security doesn't contribute to the deficit.

Yet here (I have bolded the sentences for ease of viewing):

June 27, 2010
Remarks by President Obama at G-20 Press Conference in Toronto, Canada

http://www.whitehouse.gov/the-press-office/remarks-president-obama-g-20-press-conference-toronto-canada
And we have set up this fiscal commission who will provide reports starting in November -- and one of the encouraging things, although there was resistance, ironically, on the part of some of the Republicans who originally had been co-sponsors of legislation to create the fiscal commission and they, in fact, ended up voting against it -- what’s been encouraging, based on what I’m hearing both from Democrats and Republicans, is that there’s been a serious conversation there. People are looking at a whole spectrum of issues to get at what is basically a structural deficit that preceded this financial crisis.

Even if -- the financial crisis made it much worse, but even if we had not gone through this financial crisis, we’d still have to be dealing with these long-term deficit problems. They have to do with Medicaid; they have to do with Medicare; they have to do with Social Security. They have to do with a series of structural problems that are not unique to America. Some of it has to do with an aging population. And we’ve got to look at a tax system that is messy and unfair in a whole range of ways.