Well, I don't know about the USA, but here in the UK now that we have civil partnerships it appears that society might actually save money on social security. Here's why:
Before civil partnerships, a married or non-married hetero couple cohabiting would be assessed jointly for any benefits claim, and if one was working and earning above a certain level the claim would be unseccessful. If both claimed they would not receive double a single persons claim.
Before civil partnerships a gay couple living together would not have joint assessment, so one could claim irrespective of the other's earnings, and if both claimed they would receive more money than a hetero couple.
Now, a gay couple will be treated exactly the same way as a hetero couple. As an example, last year my partner had a brief period of unemployment and was able to get benefit. Now he wouldn't even bother to fill in the forms as my income is way above the level at which benefits stop.
Solution - institute a proper health care system.