NJ does not recognize common law marriage. But for social security purposes this does not really matter, because this is the law:
"Section 1614(d)(2) of the Social Security Act provides that:
"In determining whether two individuals are husband and wife for purposes of this title, appropriate State Law shall be applied; except that . . . if a man and woman are found to be holding themselves out to the community in which they reside as husband and wife, they shall be so considered for purposes of this title notwithstanding any other provision of this section."
Section 416.1005(a) of Regulations No. 16 reads in part as follows:
"Two individuals may be considered to be husband and wife for the purpose of determining that one is the spouse of the other under title XVI of the Act if at the time the application for payments is made or at any later date:
(1) The individuals are living together in the same household, and holding themselves out to the community in which they reside as husband and wife. . ."
Section 416.1003(b) and (c) of Regulations No. 16 in this regard reads as follows:
"For purposes of this subpart, the term "household" means one or more individuals living as a family unit in a single place of abode . . . A man and woman are 'holding themselves out as husband and wife' if they represent themselves as husband and wife (or as married to each other) to relatives, friends, neighbors, or tradespeople with whom they do business."
...
Once it is determined that claimant and Eve are husband and wife, whether common-law or otherwise, or whether or not recognized by the State in which they reside, the application of the deeming provisions of the Social Security Act must follow. Subject to certain exclusions in the Social Security Act, the income and resources of Eve will be deemed to the claimant. "
http://www.ssa.gov/OP_Home/rulings/ssi/01/SSR76-27-ssi-01.html
Therefore it could be that for social sexurity purposes a relationship can be recognized as husband and wife even if the state does not recognize common law marriage.
But there are very strict requirements to it, so if you really are interested in this, you should consult an expert in social security law.