It's Medicare that's in trouble, not Social Security. As the article notes:
The trustees, issuing their once-a-year analysis, said the resources in the Social Security trust fund will be depleted by 2041. The reserves in the Medicare trust fund that pays hospital benefits were projected to be wiped out by 2019.The difference between the troubles of Medicare and Social Security is like the difference between a crack in my bath tube and a crack in the Three Gorges Dam.
Here's a 2007 graph (courtesy of the GAO) that illustrates how Medicare, Medicaid, and Social Security spending is projected to rise in future decades. The graph makes it clear enough which programs present major policy challenges for the country, and which don't: