Can my husband get spousal support from me?

Before the separation I worked only part time making a few dollars a week. Husband did not work at all because he was retired. Six months after the separation I got a full time clerical job making just enough to get by on my own. Now he's threatening to get spousal support because I'm working. I bring home the same amount of money he gets in social security pmts, so we're even steven on income. What are the chances he could get spousal support from me? I live in CA, he moved to TX, we were married 20 yrs.