On a national level, our social support system is weakening due to lack of funds. States are looking for ways to roll back health care and retirement benefits for state workers, Social Security funding is shaky over the long term, and Medicare may be insolvent in the next ten years without major revisions. I think I could also safely say that the foster care system in the US is, on the whole, a wreck.
The answer to this question will vary greatly from person to person. Each person has their own social support system and different people's systems will be of different strengths.
In the United States as a whole, you can argue that our social support systems are weaker than those of people in many other countries. Our society is much more atomized than some because most of us do not have large networks of people who are close enough to us to be called a social support system.
For example, many Americans live far away from their extended families. This robs them of a source of support. In addition, many Americans today have no relationships with their neighbors. In times past, people tended to know their neighbors and to be available to help them through hard times. This is much less common today.
In these ways, you can argue that the social support system for the average American is not very strong. However, this will of course be different for different individuals.