Severe anxiety can certainly provide a basis for Social Security disability. Anxiety is among the SSA's listed impairments - please see listing 12.06.
I had a hearing last week for a claimant suffering from severe anxiety with agoraphobia. This claimant has been basically housebound by anxiety, and leaves the house only for doctor appointments. Her husband does the food shopping. She buys her clothes online. It was quite clear from her hearing testimony that anxiety was severely limiting all aspects of her life, and employment was not a realistic possibility. Further, I was able to obtain a medical source statement from her treating psychiatrist that assessed severe limitations. The judge found that the claimant met listing 12.06, and issued a bench decision granting the disability claim.
For more information about anxiety and social security disability, there is a link on the sidebar of this site (in the Important Topics section) to the Claimants with Mental Impairments page, which discusses the issues involved with Social Security disability claims involving anxiety and other mental health conditions.
If you are wondering if your anxiety or other mental health condition is severe enough to receive disability benefits (and you live in Maine or New Hampshire), ask for a free Social Security claim evaluation.